Is there an increased chance of conceiving twins after taking drugs for ivf/egg donations?

Yes. Clomid (clomiphene) raises the multiple rates to 8% ( 99% twins ) from 2% general population. Femara gives a multiple rate of 5% and gonadotropins are about 15% ( 95%twins). Ivf and donor egg ivf is dependent on the number of embryos transferred, but can range from 2-30%.
Yes. It is true with ivf or egg donation will increase the chance of twin pregnancy. The reason is that with high dose fertility drugs, will produce multiple follicles and results multiple embryos. If doctors transfer more than one embryo, the chance of twin or multiple pregnancy will increased. With egg donation, the egg quality is very good, so the twin gestation will be even higher.
??? I am assuming you were an egg donor in the past in answering this question (?). Previous fertility treatments will not increase your chances of having multiples. Drugs taken for infertility treatment only effect the current treatment cycle. So have no fear about being the next octomom when you try to conceive after stopping fertility therapy.
Possibly. If you have taken fertility medications to stimulate your ovaries for ivf in the past, this does not change your chance of twins currently. Spontaneous twins occur in <1% of pregnancies. However, if you take fertility medication during the cycle you conceive (e.g. Clomid, femara, or 'injectable' medications like gonal f, (follitropin alfa) menopurj, etc) you certainly can increase the chance of twins.