on line 20 of k-1 there is a links for code 20 z. you need to use it and yes its gets very confussing the way TT laid out the its tax form. use section d1 of k-1
a composite return is when the entity files a tax return in states it conducted operations but the partners aren't residents pays the partner's share of state income taxes.
you enter your share of taxes paid and other info on your state return as taxes paid to other state. how and where you enter it on state return depends on the state
many times if line 20 contains lines that you can't enter it's becuase they are not meant for individual returns but without knowing all the details i can't be sure