There isn't a rule, but many guys will wait. If you thought the date went well, there is a good chance that it did. Don't come to the conclusion that he is not interested even after 2 days. If you are still wondering, text him again and see what his response is. If he drops off the face of this Earth, then forget it.
I very recently went through something like this, myself. Whereas every situation is different, I think in cases like this you should always just listen to your gut instinct. Chances are, he may not be very interested... otherwise, I would think he would want to at least tell you Good Morning.
Ugh. That is for middle schoolers who are immature and dumb and shouldn't be in a relationship. There's nothing wrong with texting the day after. I would. If you like someone, then obviously you'll want to talk to them. As long as the texts aren't obsessive and when he doesn't reply you text him like 5 times throughout the day, then you're good.
There are no rules when it comes to texting. Everyone is different when it comes to replying. Some reply at anything immediately. Some look at the message and wait for a long time because they don't know what to say... Don't overthink.