The parts required to be able to have periods are the same parts that are required to make babies, namely the reproductive organs (ovaries, uterus, fallopian tubes). As they are until now not routinely transferrable/transplantable between individuals - they seem to be getting there with mother-daughter transplants, but I must admit I am not up-to-date on that development - there's no way of genuine periods, although some individuals might be inclined to fake it, just like natural born females might.
So, no, M2F transsexuals have no way of producing proper periods, as the parts required to do so are plain not there. Sexual intercourse can still be anywhere from horrible to awesome.
Now that we're clear about producing proper periods (which is a resounding no, not at all!), it has to be noted that M2F transsexuals and their surrounding random humans can very well experience something very much like PMS and other 'special' times of the month/week/day, thanks to hormones. If M2F transsexuals stick to the daily/weekly/monthly dosage of, I think it's mostly just anti-androgens and estrogens now, they're pretty stable (mental illnesses not taken into account). If M2F folks are lazy, they can go into menopause every other week, or a dozen times every day, mostly between breakfast and lunch, lunch and dinner and dinner and breakfast.
If doctors are into human experiments or give in to the not too directly self-destructive cravings of their patients, the female cycle can be mimicked by timely application of estrogens and progesterone. This could even lead to M2F transsexuals producing breast milk, although I would assume it wasn't quite ready for baby (or any) consumption due to elevated hormonal levels. But that's just me guessing there.
As for your second question - F2M transsexuals usually don't come with the very manly cock'n'balls combo. Some want to go for it, others keep their original bits in their pants. In some places, they will have to have their naughty bits removed (ovaries/uterus) in order to apply for name and status change. As in the case of the curious Mr. Beatty, he decided to keep his woman bits and even got pregnant, which is a bit of a mindwarp, and takes some rather dedicated doctors to make sure the baby isn't flooded in manjuice for the nine months it usually takes our kind to reach that ripe-and-ready state in order to be flushed into the world. Most F2M I know of have their internal female bits removed, and the external organs are sewn shut, much like Muslim women in certain regions. Only that they usually keep their bits shut and won't have to endure them being ripped open at every next best childbirth party.
I hope that answers your questions, I need a shower now. No, make that a bubble bath.
