You asked many good questions, and I'll try to answer as much of them as I can.

Number one: lifespan of Soviet tanks in battle. Like you, I've seen many such estimates thrown around, they're usually presented as "well the Soviets knew that their tanks would only last for X hours on the battlefield so there was no reason to build them to run for more than X hours". I have never seen a source given, nor have I found any agreement on what X should have been even in Soviet primary documents. I researched the expected service life of the T-34 the most, and these numbers can serve as an example the Soviet attitude towards tank reliability.

To start, the T-34's engine was expected to run for 100 hours and the running gear was expected to withstand 3000 km of driving. In reality, the cast track links didn't live up to the army's expectations and lasted only for 1500 km. Factory #183 promised to resolve the issue and deliver a set of spare tracks with every T-34 they shipped. In the spring of 1941 a T-34 was expected to put out 150 hours or 2000-2250 km of runtime before the clutch or engine gave out. By this time, the Red Army issued a requirement for a 250 hour engine lifespan (2.5 times of what was satisfactory just a year prior!) with the same 3000 km requirement for the running gear. This wasn't all: the goal for 1941 was actually to develop an engine that ran for 500-600 hours and the T-34 was now expected to run for 7000 km without refurbishment. This lofty goal was never met, but it gives us some idea about the army's tendency to up reliability requirements. There doesn't appear to be any predetermined ceiling where the tank was considered "reliable enough". Improvements in reliability were considered to be important as the war went on, to the point where poor reliability of the SU-76 was one of the main reason that Zaltsman was removed from the post of People's Commissar of Tank Production despite his outstanding achievements in the role.

Engine hours or kilometers driven don't really translate into months on the front line or hours of combat, but then again it really depends on where you end up and when. Given that the army continuously requested increases in lifespans measured in hundred of hours, I don't think that they had such a low expectation of their own tanks once they entered battle, if any such number was ever arrived at.

Unfortunately, I don't have data on how long it would take a particular crew to lose a member, studies of survivability rates if the tank is hit typically determine odds of successful escape from a destroyed tank. I have some data on escapes from burned out tanks here but I don't know if you should take it as gospel since it covers only a handful of units in one specific offensive operation.

Number two: how prestigious was a tanker's service?

Starting in 1941 there is a big shift towards improving the prestige of service in the tank forces to reflect the amount of training required to operate a tank. For instance before the war you might have seen a Yefreitor (PFC) as a tank commander, but in the fall of 1941 the ranks of tank crewmen were strictly regimented. A tank commander would be at the very least a Starshina (highest enlisted rank) or an officer for medium and heavy tanks. Drivers of tanks were also highly skilled and received high enlisted ranks. Drivers in photographs often display the "Excellent Tanker" badge as well, awarded for excellent knowledge of operating and maintaining materiel. Four mastery classes were introduced for tank drivers, with bonuses to their salary for the top three (Master, 1st, 2nd). Big payouts were not atypical for tank forces: evacuation and repair of your own tanks as well as destroying enemy tanks could earn your crew significant bounties. A tanker's service was well rewarded both with accolades and money.

Number three: how did I get to the front and how long will I stay?

This is a more interesting question. If you arrived at the front during the Battle of Kursk, odds are you won't take part in it, but rather in one of the followup offensives. Hastily throwing green units piecemeal as they arrive at the front was a common mistake of 1941 that was largely (but not entirely) eliminated by Kursk. Even the reserve armoured units had arrived months prior to the battle.

As for how you arrive, it would be either as a part of an already established unit or you would be coming as a part of a reserve unit to bolster the ranks of a battered unit that was pulled out of the front line to refit. In the case of the former, your unit would be stationed somewhere deep in the rear and undergo exercises to improve cohesion (as well additional training, as officers were often dissatisfied with the quality of their reinforcements in some respect). These units would then travel to their staging areas together with their tanks by rail and then on their own power. Sometimes there would be additional training on location if time permitted, likely not. In case of the latter, you might see combat significantly sooner. I have documents about such an experience of the 70th Tank Brigade on hand, and they fit your scenario, so I'll describe what happened to them.

The 70th TBr began its fight in the Orel Offensive Operation (the offensive that capitalized on the German's failure to pinch off the Kursk salient) on July 12th, took heavy losses, and was forced to withdraw relatively quickly. Reinforcements from the 54th and 160th Reserve Tank Regiments began arriving starting on July 22nd with M4A2 and Valentine tanks in tow, the brigade's repair crews also recovered five T-34 tanks to go with them. New commanders were assigned from Front reserves. They noted that the arriving regiments had already undergone cohesion exercises before arrival, which explains the relative haste in re-committing the unit into action, which was done on July 27th. The brigade was tasked with rapidly breaching the enemy's defenses in order to capture a crossing over the river Nugr before it could be demolished. They succeeded in capturing and defending a crossing until reinforcements pulled up, but at a terrible cost: 38 tankers were killed with many more wounded, almost all of the 53 tanks on hand at the start of the offensive were either damaged or burned up. The brigade wasn't taken out of battle as a result, but rather reassigned to hold the crossing and patch up, two weeks later they were pulled out to the rear to refit again. This is obviously not a statistically significant example, but it's a good demonstration of what could happen: you could very well die in your first battle, but probably not, even in an attack that was rushed and barely succeeded.

For memoirs of Russian tankers, there is no better project than I Remember. The English section is a small sliver of the data accumulated within this site, but it might give you some idea about the spirit of the era.

Hopefully that answered some of your questions!

Sources:

https://www.tankarchives.ca/2019/05/the-myth-of-disposable-t-34.html

https://www.tankarchives.ca/2020/12/weakest-link.html

https://www.tankarchives.ca/2019/05/production-trials.html

https://www.tankarchives.ca/2019/04/the-new-t-34.html

http://www.tankarchives.ca/2019/03/wishlist.html

https://zen.yandex.ru/media/yuripasholok/horoshii-narkom-5fd648e233ed420c3f9bbec9

http://www.tankarchives.ca/2015/08/repair-rewards.html

http://www.tankarchives.ca/2018/07/repair-rewards.html

http://www.tankarchives.ca/2018/09/evac-rewards.html

http://www.tankarchives.ca/2018/07/mastery-badge.html

http://www.tankarchives.ca/2018/09/specialists.html

http://www.tankarchives.ca/2018/06/ranks-and-posts.html

http://www.tankarchives.ca/2013/07/is-2-vs-big-cats-at-lvov.html

https://warspot.ru/16544-amerikantsy-na-severe-ognennoy-dugi