Finding simpler equivalent regular expressions
A better approach would be to understand what words do these regular expressions represent. For example, what words are in $(r+\Lambda)^*$? They look something like $r_1r_2 \Lambda r_3 \Lambda = r_1r_2r_3$, where $r_1,r_2,r_3$ are generated by $r$. It seems that $\Lambda$ isn't making much of a difference. This should help you simplify $(r+\Lambda)^*$. The same approach works for the other expressions (including the first one, which you haven't simplified completely).