You have totally 418 groups as follows:The groups G1 0f size (8*22=176) will be: G(1,1),G(1,2),...,G(1,176) and the groups G2 0f size (11*22=242) will be: G(2,1),G(2,2),...,G(2,242) then enter these groups in SPSS data editor as a one variable (name= Group) and typing numbers from 1 to 418 under variable group. The next column enter the corresponding values for each group(from 1 to 418) .Due to there are some groups are not satisfying the normality test, you will use the steps: Analyze---Nonparametric Tests---K independent Samples---Choose the test type in box"Kruskal-Wallis H" then enter the the variable in the box's Test variable list and factors variable(group) in the box's Grouping variable click "OK" you will see the result of the value Sig. of comparing all groups. Note if you want dividing or separating  the groups in different column, you can do that and run new comparing for determined groups by the same above method "Kruskal-Wallis".

You have a mixed design so you only need to assume homogeneity of variance for the two group variances for the between subjects comparison. For the repeated measures factor the relevant assumption is sphericity. This is almost certainly violated as you have so many groups - but you can check the epsilon estimates for the effects of interest (which should be close to 1 if sphericity is violated and close to .047 if it is very badly violated). A further wrinkle is that a mixed design assumes multisample sphericity - so it effectively assumes the covariance matrices of each group are similar to each other (which is not to easy to check).

If I were analysing these data I'd consider a multilevel model to model session as a continuous effect and to model the covariances separately for each group (maybe fitting quadratic or cubic effects of session). Having a factor with 22 levels feels a bit messy.

Mauchly's sphericity test should be performed in the case of anova with repeated mesures.

The short answer is no. See these notes:

https://www4.stat.ncsu.edu/~davidian/st732/notes.html

Best, D. Booth