I realise that "the Roman army" is somewhat vague, so the timeline that I am most interested in is more along the lines of the Pax Romana period.
I am wondering how high or low a chance it was in order to survive a whole 25 years in the Roman army as an auxiliary. Which I understand was the time demanded in order to become a citizen of Rome.
It is not just a full tour of duty that I think when about this. auxiliares who were given citizenship as a reward for some action in battle or under a different circumstance.
Sorry if my language is a little clunky, I am not a native speaker.
There is no hard data on this, so I'm afraid I can give you none. However, I can tell you a bit about what we know, how we know it and what that tells us about the probable answer.
I have written about the length of service in this thread, the short version is that service would often have been longer than 25 years, and usually between 27 and 35 years before Hadrian. It was not a hard rule that you got your citizenship after 25 years, it was a special honour customarily granted to you on your release by the emperor, whenever that happened to be.
For the pax romana, we can neglegt battle attrition, which has been estimated to be as high as 2,6% for Republican times (see Rosenstein, Rome at War, 2004) and 0,8% for the first and second century A.D. (Scheidel, Marriage, families, and survival in the Roman imperial army:, 2005). However, the Illyrian and Germanic campaigns still led to battle losses - of course only for the involved units, so this is hard to generalize for all auxiliaries.
One easy method is to use life tables, which give rough, generalized ideas of how many of an age cohort would die within a year and of the life expectancy. While its true that ancient life expectancy at birth was skewed by high infant mortality, it's not like you could be certain to live to a ripe old age once you passed childhood - life expectancy at age 15 was ~50, which is 30 years lower than today. So we can expect a good amount of natural attrition during a soldiers length of service.
If we use such a model table (Frier's in this case) and calculate for 100 soldiers entering at age 20, we can expect about 56 of them to still be alive at age 45, or 44 to have died by natural causes. This drops to 48 survivors 5 years later. So even not counting any other influences, we already have little more than half alive, if everything runs normally and no war, insurrection, plague or border skirmish happens. Epigraphic evidence for the legions suggests that their rate of attrition in peacetime was roughly around 50%, so not significantly different from the general population (some fluctuations can be explained by promotions and transfer to elite units). Roman army barracks generally had amenities such as baths, latrines with water-flushing and washbasins or infirmaries that would help with preventing or curing disease. This would of course also be slightly different from region to region.
On your second point, since the Roman citizenship always remained a gift of the emperor (even to those who served their full term, so it could as well be withheld - and there was no legal right to enforce it - note also that this custom only started with Claudius!), units could be bestowed that honour prematurely (ante emerita stipendia; for an example the military diploma CIL XVI, 160), even on the battlefield - as was the custom before handing out citizenship to veterans became the norm. But to estimate this for the imperial period would be very hard. There are a number of surviving military diploma which contain this formula, mainly from Vespasian and Trajan, one unit which was distinguished in this way was the cohors I Brittanorum in the Dacian wars, but to say exactly what the demographic makeup of that unit was at that point of time and what your chances were is impossible to say. It happened, but rarely, so I would estimate a very low number. Individuals might also be granted the citizenship out of order, but that is statistically insignificant.
So if I had to give you a number, I'd say your chances were around 50%, if your unit didn't go on campaign during your service - if you were part of one of the auxiliary cohorts that joined Varus on campaign in Germany, or one of the auxiliary units in the Batavian insurrection, your chances would plummet rapidly.
Edit: spelling