“Do trans women generally have a physical advantage over women?”

No. Trans women were able to complete in the Olympics beginning in 2004. No trans woman has won an Olympic medal in the woman’s category.

There are many studies that compare cis men to cis women and based on that claim trans women have an advantage. Among the studies that actually compare trans women to cis women it is generally found that trans women have no overall advantage.

“Are there any rules for this kind of thing? Do they need to be transitioning or taking suppression drugs?”

The rules and requirements vary by league. At higher levels of competition its generally required to have hormone levels at cis female levels for a prolonged period. Often 6 months or longer. To clarify, getting to those levels roughly takes 2+ years of hormone replacement therapy(hrt). Hrt for trans women generally consist of an anti-androgen, estradiol, and progesterone.

I’m not sure why you assume it’s one or the other. My money is on both. Probably has a whole library to choose from…