Welcome to the STD forum. Sorry to hear you caught herpes. However, in the long run it probably won't be a big deal for you, because recurrent outbreaks and sexual transmission are much likely than for HSV-2. Here is a thread that goes into this in detail:
http://www.medhelp.org/posts/show/969931
As to how you caught your infection, most likely it was by oral sex; probably your former partner has oral herpes due to HSV-1. Whether the "small mouth ulcer" was herpes or not is hard to say, but it is possible. However, it sounds possible his genital burning and "red spots" were herpes and that you are one of those infrequent persons whose catches genital HSV-1 by vaginal intercourse. Most likely you'll never know for sure.
1) I know nothing about beetroot and have no idea whether it can cause genital burning. But I doubt it.
2) Genital to genital HSV-1 transmission is uncommon, but of course it occurs from time to time.
3) If your partner had genital HSV-1 and that was the source of your infection, it is likely he acquired it recently. But not necessarily.
If you are still on good terms with your former partner, you could speak with him and try to learn more. If he got professional care and had a definite diagnosis of either genital or oral herpes, and if it is known whether the infection was initial or recurrent, that would help sort out these questions. Without that information, you're never going to know. But at this point, I don't see that it matters. While I understand your curiosity about it (and about whether he had sex with other people), at this point it makes no difference with respect to your herpes.
I hope this helps. Please read the other thread on genital HSV-1; you should find the information reassuring.
Best wishes-- HHH, MD