Welcome to the forum.
This is clearly a risky situation with respect to STDs. But contrary to your apparent assumptions, the STD risk has nothing to do with your buddy and his sex with the same partner a day earlier. Your female partner is the problem: she clearly is someone who is minimally selective, if at all, about her partners, and has sex with casual partners, sometimes (often? usually?) without condoms. A woman like her has a very good chance of being infected with chlamydia, HSV-2, and HPV; and perhaps a fair chance of gonorrhea as well. The risks of syphilis and HIV are low, however.
So on that basis, you ought to be tested for STDs. Consider visiting your local health department STD clinic for highly expert, confidential evaluation and testing. Most likely you weren't infected, even if she is; most STDs are not efficiently transmitted -- i.e. even if she was infected, the odds are in your favor. But of course better safe than sorry.
As those comment suggest, the specific questions you ask are not very important. But the answer to no. 1 is that 24 hours is too soon for her to become infected and then have the infections progress to a point they could be transmitted. Even if your buddy has any of several STDs, you are not at risk on that account. But if you remain concerned about it, you could speak to him and suggest he go for STD testing when you do yourself.
As for HIV, it's not a serious consideration in this situation, unless you (male) friend is bisexual, or if either he or your (female) friend use drugs by injection. If not, I really wouldn't worry about HIV. But since you ask, here are two threads on the HIV Prevention and Safe Sex forum that go into detail about timing for reliable test results. The bottom line is that for an antibody-only test, 6-8 weeks is enough time; for the antibody/p24 "combo" tests, it's 4 weeks. (Read all of both threads; some of the main information is in follow-up comments.)
http://www.medhelp.org/posts/HIV-Prevention/-A-Question-on-Testing/show/1347755
http://www.medhelp.org/posts/HIV-Prevention/Need-your-help/show/1345664
My final comment concerns your apparent dismay/shock that your buddy had sex with the same woman you did. Your wording -- suggests she is a friend that happens to be female, but not your girlfriend in the romantic sense. If so, what makes your (male) friend any less responsible to you (or less a friend) than you are to him?
Anyway, I hope this puts things into perspective for you and is helpful.
Regards-- HHH, MD