OP, you can sleep with someone whenever you want! It's absolute gobshite that you need to wait for a certain amount of dates. Human nature means that if he's a douche who only wants sex, he'll dump you whether that happens on first date or fifth. It's puritanical nonsense from people who don't think women can actually have sexual appetites themselves.
I personally won't wait longer than second date, as sexual chemistry is important to me, and i don't want to emotionally invest too much in someone to find out the sex is awful. But you do it when you feel ready! Only tip, if you do go back to his don't hang around too long in the morning unless he explicitly asks you. Enough for a quick coffee and then be off (unless he suggested breakfast). It can really ruin memories of a nice night when someone won't leave and you want to get on with your day, but you can't be rude and tell them to either.
There are no other rules to dating other than, if he hasn't called you his gf, you are single and can date others. In fact you should, so you don't get too emotionally invested and then hurt (eggs all in one basket). But also you should, so you can figure out what YOU want. Too many women make the mistake of falling for guys just because they respond quickly, set dates, aren't complete shits - and forget to consider if his personality and life are actually suitable to them. Don't fall for a guy just because he's nice!
Don't take rejection personally - you won't be everyone's cup of tea, that's ok. Let him message you like he promised and set that second date. If he's dithering, don't chase - just set up other dates for yourself. If a man likes you, unless he's really socially awkward or shy, he will want to get a date locked in.
Have fun!