Question

how are paired t-test similar to repeated measures ANOVA?

Answer 1

They are equivalent..the assumptions for both are same...it is sometimes indicated that the assumption you cite for anova ,when met do cover the normality assumption for paired t test..as both are equivalent "bivariate" repeated measures anova works as well if only the differences are normally distributed...the more strict repeated measures requirements in the literature are only necessary if more complicated layouts with more factors and other hypothesis are included...in particular between subject factors and unequal sample sizes between them...