1- Tacitus likened him to Alexander, but this is partly a result of Tacitus' critical view of the Julio-Claudian dynasty and hid elevation of Germanicus to the role of a purer type of Roman, something that could have been bit never was. Germanicus was a capable general but never conquered any territory for the Empire, and so does not bear comparison to true Roman greats like Caesar or Pompey, let alone Alexander, history's first long range conqueror.

2- Germanicus was clearly a capable general, he managed to manoeuvre Arminius into fighting a major pitched battle, which the latter was deliberately avoiding, and then he won that battle. He carried out his campaign competently and despite some near misses (especially under Caecina in AD 15) avoided any major reversals against very capable opponents. He was clearly figure well respected by the soldiers as evidenced by his being sent by Tiberius to quell a serious mutiny in AD 14. His position as a senior member of the semi-divine Julio-Claudians would have also helped his credibility with the soldiers.

3-His finest moment as general was no doubt his major defeat of Arminius at Idistavisus in AD 16. While this did not mean the Empire got the lost province of Germania back, the victory did re-establish their reputation for military dominance, which in the end was probably more important.

4- Germanicus could not have reconquered the province because defeating the German armies was not the same as reducing the area to a tax paying province. This is where the Romans were working to when the defeat of Varus scuttled the whole program in AD 9, and it took decades of campaigning to get things to that stage. The establishment of Roman communities and infrastructure was wrecked in the aftermath of AD 9 and Augustus made a policy decision after that point not to attempt to re-establish the province, a strategy which continued to be followed. Germanicus' punitive campaign was the start of a new method of dealing with troublesome German tribes and confederations across the Rhine that the Romans roughly followed for the rest of the Empire. Germanicus could have pacified the place with a longer campaign, but to re-establish the province was beyond the scope of a single campaign.

5- I have to say I can't think of any books dealing specifically with Germanicus. I'd start with that one by Goldsworthy, who is a reasonably reliable academic. There's a book by Lindsay Powell on him but I'm not familiar with the man and he's not a trained historian but rather someone who has an ominous sounding "multidisciplinary" approach so he wouldn't be my first pick. Sorry I couldn't be more helpful here.

Overall, what made Germanicus such an effective general was the fact that he had a good reputation, which translates to a good relationship with his men, he commanded experienced troops with extremely good subordinates (like Caecina) and as the heir to the throne, he was allowed to go win major victories and be acclaimed imperator without Tiberius having to worry about the legions acclaiming him Emperor. That meant he could campaign relatively free of political interference. That said, while Tiberius had a very good military reputation, it still wouldn't do to let Germanicus eclipse him (which he didn't), and it is conspiracy theories drawn from this fact that led Tacitus to speculate about the role of Tiberius in Germanicus' early death. Overall, I would personally classify Germanicus as a 'good' general, but he did not campaign for long enough against tall enough odds to be rightly compared to the likes of Alexander, Hannibal, or Caesar.