I sympathise with your state of mind, I really do. Having recently exited from a very confusing situation myself, I can honestly say I'll never quite understand how the female brain works.
My concern here, for you, is why she felt the need to tell you she's seeing another guy. If I was dating someone, and they then told me they were dating around, I'd question their sincerity with me. If they want to date around then that's their call, but they've no reason to openly tell you. if you ask(ed) then that's a different matter, but if she just came out with it, that would indicate (to me at least) that she's not as interested in you as you are in her; it's a common theme, especially amongst us guys who, as you've put it, had bad luck you get hung up on what could be.
To elaborate slightly, I've had (probably less) luck than you, so when I got a Tinder match and went on a date, I thought it went really well, and I thought the second one went quite well too - I didn't rush into anything, which may (or may not) have been the right thing to do. I do however know that I got in too deep (emotionally) which may have resulted in us going our own way (her call, though thinking back on it, she probably figure I was too emotionally invested and she wasn't sure what she wanted).
It's a complicated scenario; some girls would rather date and take their time, whereas others are quite happy to jump into action straight away (films, tv shows and social media typically imply it's always the former, when that really isn't the case at all). Finding out the right speed to go is a friggin' minefield.
I'd agree with this, and (on the rare occasion I am dating) I'll not multi-date. I wouldn't want it done to me, so don't do it to other people, though am aware that the people I've dated may have gone on other dates whilst dating me. It's never played on my mind (until the latest one) but ultimately if I don't know about it, it shouldn't be an issue. As you've stated though, there's nothing you can do about it, though it sure is a ****ty feeling to have.