OK. I think everything is possible.
But regarding two simultaneous melodies, particularly if the two are equally relevant (principal), it's better that they "take turns".
Take a look at the master of masters: Bach, the first invention (two voices). Whe one is active, the other one is less active and vice versa.
So basically counter melodies are only possibe if the main melody sustains long notes or stops playing altogether?
What I tried to do there with the last four chords before it went to E min was I - V - IV - IV/iii
In the last chord I added a E note underneath it...or was I suppose to add the E min chord under the F chord?
Your transition to E minor was quite good! I would put a little more emphasis on the B since that's the V of iii, and to put a little more attention onto it.
Suspensions: The general rule for suspensions is that the note you're trying to resolve to is not also present in the suspension. You also shouldn't be resolving to a 13th tone unless it jumps to that new key. Things for you to think about. Nice!
What happens here is that the melody never rests. It's good you leave moments of "silence", there you can write a countermelody.
In general terms, when there are two melodies, when one is less active (long notes, rests) the others is responding.