For (1), do you mean "lexical category"? If so, the relationship between c-selection and lexical category is that some morphemes only combine with roots/words/phrases that have a particular lexical category, and we call this type of restriction "c(ategory)-selection." So c-selection is defined in terms of lexical category.
There technically is no relationship between lexical category and s-selection; some morphemes only combine with roots/words/phrases that have a particular semantic property (i.e., meaning), and we call this type of restriction "s(emantic)-selection". S-selection, unlike c-selection, doesn't care about lexical category, it only cares about lexical semantics and compositional semantics.
(2) Grammatical aspects (like progressive, perfect, simple) differ in their (i) acceptability and (ii) interpretation, depending on the lexical aspect of the VP they combine with. These differences can tell you what the lexical aspect of the VP is.
For instance, let's say you do not know what the lexical aspect of "remember the answer" is - is it a stative, activity, accomplishment or achievement? You can test this by combining the VP with the simple aspect, because we know that the simple aspect gets (i) an ONGOING interpretation with stative, but a (ii) HABITUAL reading with other lexical aspects. So you check "She remember-s the answer" and find out it has the ONGOING interpretation. This tells you that "remember the answer" is a stative.
Other examples of this are in the slides about lexical aspect (week 10, I think)
Hope that helps,