For the non-parity cases, almost all of them can be solved with some variation of slice flip slice. When it looks like you have a 2-swap, put the edges at UB and UF and do Rw2 F2 U2 Rw2 U2 F2 Rw2.
For the parity cases, many of them can just be set up to another by doing R U R' F R' F' R, and if you don't want to learn to many algs, I think you only need about 4 or 5.
If you don't know how to differentiate between parity and non-parity cases, this should just come with time if you do enough solves.
I have looked before, and unfortunately I do not know of an L2E trainer - you'll probably just have yo keep reviewing your algs until you definitely know them.
Personally, I average about 1:30 on 5x5 - I only know the non-parity cases and the parity alg.
Good luck!