Roof:
Like you I am struggling with the last few, despite all the help from everyone for which thanks.
LHS 8ac, Synonym for extra outside synonym for rest, definition dramatist, (not English)
5d, Yes, an island which is divided into two countries.
20ac, As previously noted, synomym for peculiar in one sense, and a type of ad. Adding I leads to an anagram of an unusual two-word phrase.
4d, Double definition, species of eagle and monster.
6d, His country's sounds like girl's name
11ac, I think your R is wrong. I haven't fully parsed it, but the hydrocarbon seems to be a paint solvent with letters removed, D added, and the only anagram.
Now for my problems:
2d, LH and RHS;
7ac RHS
13d LH and RHS
That's not all I am still missing, but hopefully it will be enough to get the rest.