Stat theory is definitely on topic here.
Yes, there's some overlap with math.SE, just as there is with some computational statistics questions vs similar questions on SO; indeed that same issue exists at the boundaries all over the SE network. In the cases where something is on topic in more than one location it belongs at the one you choose to post it at.
Note that you are requested in the help not to cross-post to multiple SE sites:
Please note, however, that cross-posting is not encouraged on SE sites. Choose one best location to post your question. Later, if it proves better suited on another site, it can be migrated.
Are there any general guidelines available for deciding on which Exchange to post?
I'd start with the description of what's on topic in the help for both sites, and on the extent to which particular types of questions tend to be well-answered. (Some people are active on both sites.)
Is there anyway to search both Exchanges simultaneously?
I don't know of any way to do it, but copy-pasting the same search into two tabs isn't terribly onerous. I do it ... well, not frequently, but sometimes.
Edit: Actually, of course there is: Google certainly indexes both sites, and I've had answers on both pop up in Google searches. If you use the
site argument in a Google search in such a way as to include both, you should be able to search both that way. Google seems to update on the content of the two sites within an hour or so, so it's always pretty current. (Some equivalent on some other search engines will probably also work, but I haven't tried.)
Finally, is there anyway to combine profiles and reputation points? (not a biggy, it would just be nice to have Mathematics reputation points on Cross Validated)
No, you can't combine your reputation on both. But if you have enough reputation on one, you can get an association bonus on the other - which helps in that you don't have to build up the low-level reputation - so if you do that you can start commenting and such, right away.
See here, where it says:
You gain reputation when:
- you associate accounts of two or more Stack Exchange network sites, and at least one of those accounts already has 200 or more reputation: +100 on each site (awarded a maximum of one time per site)
I believe you can use the one profile for both, though (but what you do at each site doesn't carry over).
[On the other hand, when you use chat, you will have your combined SE-network reputation show; when I am in chat presently, mine shows as 38K not 36K because I have a couple of thousand reputation between StackOverflow and math.SE]