It's hard to answer your second question since you have not given complete description of your monomer. Since you need diamine, your monomer must have one amine and a nucleophilc center (which must be more reactive than amine) or just have two nucleophilc centers. Either way, if you are doing your reaction in small scale, stirring (you called it agitation) is important to complete the separation of solvent (dimethylacetamide, which may dissolve in methanol/water) from product and to dissolve extra $\ce{K2CO3}$ so that you have only crude product in remaining solid material. If you are doing your reaction in large scale, then it is a different story.
One needs to know the your monomer structure to determine amount of $\ce{K2CO3}$ needed for the reaction. For example, if you have more acidic functions in your monomer other than reactive nucleophilc centers, you may need additional equivalents for those groups. Since it is not really strong base, use of excess is always better. For example, following is the relevant polyimide preparation with two phenolic reactive centers (Ref.1):

In this case, they have used a little more than two equivalents of $\ce{K2CO3}$ in the reaction. The differences between this and yours are the monomer (may be) and the solvent (dimethylformamide vs dimethylacetamide). So, you may find some insight for your project from this reference.
Reference:
- S. Devaraju, M. R. Vengatesan, M. Alagar, “Studies on thermal and dielectric properties of ether linked cyclohexyl diamine (ELCD)-based polyimide POSS nanocomposites (POSS-PI),” High Performance Polymers 2011, 23(2), 99-111 (https://doi.org/10.1177/0954008310391825)