All M. structor's aren't clones, only in that colony.

They are out their in the wild reproducing with other M. structors sexually.

I thought one of the big points was there's no M. structor females on the islands.

They've extended their range, so there's lots of cases where they don't have wild ones around, but there's still overlap, at least according to the article I read.

Yes, in some areas - but not e.g. on Sicily. https://www.youtube.com/watch?v=Z-O4_AwWpfI gives perhaps a better overview

M. Ibericus produces 4 kinds of offsprings.

    1. M. Ibericus queen + no male (unfertilized egg) -> M. Ibericus male.
    2. M. Ibericus queen + M. Ibericus male -> M. Ibericus queen
    3. M. Ibericus queen + M. Structor male -> M. Structor male, no genes from the mother
    4. M. Ibericus queen + M. Structor male -> M. Structor/Ibericus hybrid female, (worker ant, infertile)

The authors tried to find evidence of gene flow between the domesticated messor drones and the wild messor populations, but couldn’t. They sequenced about 100 ants, so it was not an exhaustive search. However if it was common you would have expected to see it.