Q: How do I include covariates in my MEMORE analysis?

A: Because the effects are estimated within person there is no need to control for between person covariates (e.g., age) since you essentially have perfectly matched pairs. However, if you want to control for a within-subject variable, you can include it as another mediator in parallel (if you think it only confounds the M --> Y path) or in serial (prior to the mediator) if you think this variable may confound both the X --> M path and M --> Y path.

Q: Can MEMORE account for more than 2 conditions?

A: Yes! Judd, Kenny, and McClelland (2001) describe how to define contrasts of interest related to more than 2 conditions.

Mediation: I recommend reading Preacher and Hayes (2014) about handling multicategorical predictors in mediation. The same issue arises for within-subjects designs. You'll have to define contrasts of interest in order to to estimate the indirect effects of interest.
MEMORE does not have any built in functions to do these types of contrasts, but if the contrasts are pairwise comparisons then you can just enter the pairs in a set of MEMORE analyses. Alternatively, if the contrasts are more complex one would create a variable that is a combination of the variables you want to compare. For example if there are three conditions, and you want to compare the average of two conditions to the third (Y1+Y2)/2 - (Y3), then you can make a variable that is (Y1+Y2)/2 = Ycont and (M1+M2)/2 = Mcont, and enter that into the MEMORE command like so:
MEMORE Y = Ycont Y3 /M = Mcont M3 /model = 1.

Please note however, that I do not recommend using MEMORE for more than 2 measurement points longitudinally. Multilevel and longitudinal mediation models can more appropriately account for the time series nature of longitudinal data.

Moderation: I recommend reading Hayes & Montoya (2017) about handling multicategorical predictors in moderation. MEMORE can be used for evaluating any contrasts of conditions and whether that contract is moderated by a predictor variable. For example, if there are four conditions, and you want to compare Condition 1 and Condition 2 (together) to Condition 3 and Condition 4 (together) (Y1+Y2)/2 - (Y2+Y3)/2, then you can make a variable that is Y12 = (Y1 + Y2)/2 and Y34 = (Y3 + Y4)/2, then use MEMORE with Y12 and Y34 as the two outcomes:

MEMORE Y = Y12 Y34 /W = Mod /model = 2.