I know the mean, SD (or SEM) and sample size for each group. Which tests can I run?

You can enter data as mean, SD (or SEM) and n, and Prism can compute two-way ANOVA. It is not possible to compute repeated measures ANOVA without access to the raw data.

I only know the group means, and don't have the raw data and don't know their SD or SEM. Can I run ANOVA?

Yes, two-way ANOVA is possible if you only have one value for each condition (no subcolumns). In this case, Prism will only be able to compute ordinary (not repeated measures) ANOVA, and will assume that there is no interaction between the row and column factor. It cannot test for interaction without replicates, so simply assumes there is none. This may or may not be a reasonable assumption for your situation

I want to compare three groups. The outcome has two possibilities, and I know the fraction of each possible outcome in each group. How can I compare the groups?

Not with ANOVA. Enter your data into a contingency table and analyze with a chi-square test.

What does 'two-way' mean?

Two-way ANOVA, also called two-factor ANOVA, determines how a response is affected by two factors. For example, you might measure a response to three different drugs at two time points. The two factors are drug and time.

If you measure response to three different drugs at two time points with subjects from two age ranges, then you have three factors: drug, time and age. Prism does not perform three-way ANOVA, but other programs do.

What does 'repeated measures' mean? How is it different than 'randomized block'?

The term repeated-measures strictly applies only when you give treatments repeatedly to each subject, and the term randomized block is used when you randomly assign treatments within each group (block) of matched subjects. The analyses are identical for repeated-measures and randomized block experiments, and Prism always uses the term repeated-measures.

What is a mixed-model design?

In the context of two-way ANOVA, a mixed-model is one where one factor is repeated measures and the other is not. Prism 6 can analyze data where neither factor is repeated measures,  one of the two factors is repeated measures, or when  factors are repeated measures. Earlier versions of Prism could not analyze data where both factors are repeated measures.

My two factors are genotype and treatment, and each animal was measured at several time points. Can Prism analyze this kind of "two way" ANOVA?

No. Your experimental design has three factors: genotype, treatment and time. If you wanted to use ANOVA, you'd need to use three-way ANOVA, which Prism does not offer.