Are there currently any openings for 35N, 35F, or 35M?

The only person who can tell you that is your recruiter. Only recruiters have access to that information. Even if I was a recruiter, I had access to that information, and I told you that there were seats oh, you would still have to go to your recruiter

What branch are you going? It may be true for reservists if there are no unit slots available but it also depends on training slots for when the AIT classes begin. Right now the soonest you could ship out is January if there are available slots open. Like others said, you should check in with your recruiter often so they can keep checking.

As already said - check with your recruiter - early and often. A slot may miraculously open tomorrow morning - and be filled by tomorrow afternoon. (But don't become a pain - recruiters are human, and you want an ally, here.)
That being said, I think you need to take a look at what you really want from the Army and what you have to offer. Those three MOSs are all MI, but they are radically different. If you are looking at any of the three, you may need to re-think your ideas or sit down for a more in depth talk with your recruiter. Or maybe scan through some of the other discussions on RP regarding the basics of each MOS.