I think it would be fair to say that Belisarius had always tried to win over the local population if required, since it was a policy that made political sense for reconquered territories in the West, but circumstances often intervened, forcing him or his replacements to adopt a harsher policy. It is therefore debatable whether he pursued a particularly effective campaign to win over the hearts and minds of the population. It for example definitely did not take place on the Persian front - territorial conquest was never part of the plan in Mesopotamia (it was an important goal in the Transcaucasus, but Belisarius never campaigned there). The Persian Wars were instead dominated by sieges of important border fortresses and the sacking of settlements to deny resources to the enemy/acquire loot. Belisarius personally led several ravaging expeditions into Persia, but otherwise was mostly concerned with defending Roman territory against Persian incursions, so there were few opportunities for him to implement whatever counter-insurgency strategies he had. An attack into Persia in 541, as described by Procopius, explains this dynamic quite well. On the one hand, Belisarius ordered al-Harith, an Arab chief serving the Romans, to pillage Assyria:

Accordingly he [Belisarius] commanded al-Harith with his troops to advance into Assyria [...] and he commanded al-Harith to pillage all that lay before him and then return to the camp and report how matters stood with the Assyrians with regard to military strength. So al-Harith and his men crossed the River Tigris and entered Assyria. There they found a goodly land and one which had been free from plunder for a long time, and undefended besides; and moving rapidly they pillaged many of the places there and secured a great amount of rich plunder.

On the other hand, Belisarius also induced a fortress to surrender in the same campaign. He dealt with the captives humanely, but the point was not to pacify the region, but to destroy an important Persian frontier fortress:

And George [Belisarius' underling] succeeded [in getting the fortress to surrender], after addressing to them many words of exhortation and of kindly invitation, in persuading them to take pledges for their safety and to deliver themselves and the fortress to the Romans. Thus Belisarius captured Sisauranon, and the inhabitants, all of whom were Christians and of Roman origin, he released unscathed, but the Persians he sent with Bleschames to Byzantium, and razed the fortification wall of the fortress to the ground.

Belisarius' campaign against the Vandals provides a clearer example of an active reconciliatory policy, since the whole point of the expedition was to restore Roman control over that province. According to Procopius:

There he [Belisarius] reminded the soldiers at length of how much good fortune had come to them because they had displayed moderation toward the Libyans, and he exhorted them earnestly to preserve good order with the greatest care in Carthage. For all the Libyans had been Romans in earlier times and had come under the Vandals by no will of their own and had suffered many outrages at the hands of these barbarians. For this very reason the emperor had entered into war with the Vandals, and it was not holy that any harm should come from them to the people whose freedom they had made the ground for taking the field against the Vandals.

Soon however there were problems, though strictly speaking they shouldn't be blamed on Belisarius. He only stayed in Africa for a few months (late 533-early 534) before returning to Constantinople in triumph (but also conveniently to reassert his loyalty to Justinian, as there were reports of his treasonous behaviour being passed back to the capital). What did Belisarius actually do in the meantime? He seems to have treated the Vandals reasonably well, established peaceful relations with the Berber tribes and Justinian had even ordered that Arian Christians were to be tolerated. These successes unfortunately were only temporary: soldiers who gained Vandal lands through marriage were outraged by the policy of giving land back to their original owners, the Berbers realised that Roman control over the region was still flimsy and can be contested, and lastly the local Nicene Church hierarchy forced Justinian to repudiate his policy of reconciliation with the Arians. The next decade would be consumed by mutinies within the army and persistent warfare with the Berbers. So much so that Procopius would eventually write:

Thus it came to pass that those of the Libyans who survived, few as they were in number and exceedingly poor, at last and after great toil found some peace.

As I said, Belisarius should not be blamed for all of this, but his pacification of the region was clearly not permanent, as it must have been impossible for him to fully secure the region within such a short period of time, even if he had a clear counter-insurgency strategy in mind. The picture provided by Procopius is of course exceptionally gloomy and not particularly accurate, since there was a large amount of public building projects in this period and North Africa was largely at peace from 548 onwards, but these gains were not made by Belisarius, but by similarly talented men such as John Troglita.

The same was true for Italy. In principle it was all about restoring Roman rule to a region that had been under 'barbarian' sway for decades, but in reality it was more complicated, since the Ostrogothic state was a highly Romanised one and did its best to promote itself almost as a restored Western Roman Empire. Belisarius no doubt wanted to achieve a quick military victory, one with relatively few effects on the civilian population, but things didn't work out quite as well as it did for the North African campaign. Naples, an important city in southern Italy, was actually sacked quite brutally by his soldiers:

And then a great slaughter took place; for all of them were possessed with fury, especially those who had chanced to have a brother or other relative slain in the fighting at the wall. And they kept killing all whom they encountered, sparing neither old nor young, and dashing into the houses they made slaves of the women and children and secured the valuables as plunder; and in this the Massagetae outdid all the rest, for they did not even withhold their hand from the sanctuaries, but slew many of those who had taken refuge in them.

Belisarius did his best to restrain his soldiers, but the damage was done - Rome quickly surrendered to him, partly out of fear of being sacked by his army:

The inhabitants of Rome, fearing lest all the calamities should befall them which had befallen the Neapolitans, decided after considering the matter that it was better to receive the emperor's army into the city.

Belisarius did quite well in rallying the city of Rome against their former Ostrogothic overlords, but he also caused problems, as he had also deposed Pope Silverius, a move that cannot have endeared him to the local population. Famine and disease was now also rife in central Italy; again, not Belisarius' fault, but war was not pleasant for the local population and many historians now argue that it was the Gothic War that was more damaging to Roman influence in the region than the policies of 'barbarian' governments. Nonetheless, the war was reasonably successful up to 540 and by then the Ostrogoths were willing to make peace. Belisarius however disagreed with Justinian's suggestion of maintaining a rump Ostrogothic state in northern Italy, as he instead attempted to win a more total victory through deceiving the Ostrogoths and seizing their capital Ravenna. This naturally made many Ostrogoths very angry, leading to another 14 years of bitter war in Italy, They regrouped under a very capable king named Totila, an event that coincided with a major Persian offensive in the East and the arrival of the plague; there would no longer be any easy victories for the Romans and the optimism of the 530s would soon disappear.

Belisarius returned to Italy in 544 (after a stint fighting the Persians in the East), but he was now fighting a public relations battle with Totila, who was also doing his best to win the heart and minds of the locals. To a certain extent this even worked on Procopius, Belisarius' ex-secretary and whose works were replete with praise for the general - his attitude had however changed in the 540s and in his last book describing the Gothic War it is possible to see Totila as the protagonist rather than the various Roman generals fighting him. Belisarius was unpopular amongst his fellow generals, out of favour in Constantinople and did not have enough resources to win a total victory, so it is difficult to see how he was able to achieve any major success in winning over the local population. As with Africa, it was only when Belisarius left the theatre (549) that the Romans were able to make consistent gains again, as more resources were poured into Italy under another capable general, Narses, who was able to finally conclude the war in 554.

In short, I think it is quite difficult to answer your questions about Belisarius' policies towards the civilian population. We largely have to rely on Procopius, who was overtly positive towards the general in the early years and indifferent or even angry at Belisarius later; either way however other personalities were overshadowed by the historian's focus on Belisarius. We have a few mentions of Belisarius' treatment of the locals, but we also have accounts of his mistakes and brutality towards civilians, so I think it would be very difficult to talk about his general attitude towards the locals. Above all, Belisarius only took part in some of Justinian's decades-long wars, so it is similarly difficult to talk about how Belisarius' policies influenced their eventual outcomes.

Let me know if you have any more questions!