Ants... Soooo confusing!!

[Charlie]

Ok this is what I've got so far.

Queen has wings and when the weather is right, mates with a random male (who dies shortly after)
Queen hopefully forms a colony where her eggs become worker females whom are sterile.
She reproduces haploid males from unfertilised eggs and sterile eggs are eaten
Fertilised diploid female eggs are future queens.
Worker ants lay unfertilised eggs that (if the queen is dead) with become haploid males, as the colony is doomed.

My questions are this.
1) How can a female produce fertile males just from her chromosomes?
2) How can sterile females produce fertile males on there own?
3) Does the queen reproduce once in the colony?