In principle yes, you could in theory use micro injection to inject haploid DNA into the egg. I don't think this has been used in practice though. However Dolly the sheep was created by exchanging haploid nucleus of a sheep egg with a diploid nucleus from a mammary gland cell.
Not necessarily, DNA is packaged into chromosomes and diploid cells have two copies of the same chromosome (with the exception being the sex chromosomes MALE:XY FEMALE:XX). Remember that gametes are haploid (single copy of each chromosome) and that homologous recombination occurs during gamete formation, therefore the chance of obtaining two identical sets of haploid DNA that also match the females is extremely low, unless all chromosome pairs are completely identical.
In principle yes. I could imagine that DNA extraction from eggs could be used for artificial fertilization and the result of that would be a race of all females.