Let's first discuss what can cause odor. First, despite what many may think, your vagina has very little odor. Vaginal discharge, menstrual blood, and sweat have no malodor (a particularly strong or offesnsive smell). When these forms of discharge mix with our body's normal bacteria, odor can develop. Yes, some can get trapped in pubic hair, sit too long in our underwear, or on a pad. That said, shaving is not necessary and simply a personal preference. Vaginal hygiene should consist of washing the external portion of your vagina and surrounding area with mild soap and water daily. Never attempt to wash the inside of your vagina and avoid perfumed soaps.
I don't know, I've never tried, but I can't see any reason why it would. Just make sure you're washing your vaginal area with warm water and mild soap. If you've noticed a change in the way that your vagina smells, or you're bothered by the odor, you should talk to your healthcare professional.
Washing thoroughly with mild soap and water should be just fine. Shaving your bikini area is a personal choice, there are no medical reasons why you should or shouldn't, but I don't think it has anything to do with odor. I'd base this more on what makes you comfortable!