

No. You should analyze all the groups at once with oneway ANOVA, and then follow up with multiple comparison tests. The only exception is when some of the 'groups' are really controls to prove the assay worked, and are not really part of the experimental question you are asking.
You can enter data as mean, SD (or SEM) and N, and Prism can compute an unpaired t test or the Welch t test. Prism cannot perform an paired test, as that requires analyzing each pair. It also cannot do any nonparametric tests, as these require ranking the data.
No. The t test compares the difference between two means and compares that difference to the standard error of the difference, computed from the standard deviations and sample size. If you only know the two means, there is no possible way to do any statistical comparison.
It is not a good idea to base your decision solely on the normality test. Choosing when to use a nonparametric test is not a straightforward decision, and you can't really automate the process.
Not with a t test. Enter your data into a contingency table and analyze with Fisher's exact test.
You should use special methods designed to compare survival curves. Don't run a t test on survival times.
While that sounds like a good idea, in fact it is not. The decision really should be made as part of the experimental design and not based on inspecting the data.
No. The results of any statistical test can only be interpreted at face value when the choice of analysis method was part of the experimental design.
Ruxton (1) and Delacre (2) make a strong case that this is a good idea.
1. Ruxton. The unequal variance ttest is an underused alternative to Student's ttest and the MannWhitney U test. Behavioral Ecology (2006) vol. 17 (4) pp. 688
2. Delacre, M., Lakens, D.L., and Leys, C. (2017). Why Psychologists Should by Default Use Welch's ttest Instead of Student's ttest. Rips 30: 92–10.