Did I make a mistake from marrying them with such low levels?
You can marry them whenever you want, basically. In fact, it's better that you marry the couple that you want as soon as possible for better stat bonuses!
However with skills? To get the best skills, you'll have to start training your units in a special way to get skills for their kids. I'll talk more about it below!
Does my characters have to reach a certain level before their child appears? Or do I need to reach a certain point in the game in order for them to come?
Around Chapter 14, in which you'll see different branches throughout the world map by then, but, you have to be careful with a few of them, because obviously some of those maps are way harder than others, so, you just gotta train a bit.
What about abilities? I don't really understand those. Can someone explain passing those on? I feel like I might have made a mistake and now I won't have the strongest children from the parents that I can.
Hm, this is a tad tough to explain... Grab a chair! o/
See the Equip Skills command? The children will get their mother's and father's last skill on that list. Like for example, if you marry Chrom with Oliva, and say, Chrom has the Aether skill on the bottom of the list. Chrom's daughter(s) will automatically get Aether. There's some exceptions to this, like, Olivia can't pass her dancer skills to her son, and if Chrom has a son, he'll only get the Rightful King skill.
In a nutshell, that's the skill inheritance mechanic. There's a lot of skills, but, yes, there are some recommended ones that you should pass on to the children, for example, you're marrying Lissa to Vaike. Lissa can be reclasses to a Pegasus Knight, in which she can be promoted to a Dark Flier, who at level 15, has the Galeforce ability, which allows you to move again after killing an enemy unit. And see here's the thing; only certain Female units can get that class, because it's exclusive to being part of the Pegasus Knight class. So, in other words, I recommend that you try to train up Lissa before reaching the map with Lissa's son, so he'll be able to get that skill too.
But don't get me wrong; getting certain skills for them, that's just how you can get your children to be the strongest they can be. That's not to say the children aren't stupidly strong already; you just have to train them up, because you'll find them at level 10. Children's base stats and growth rates are the same as the mother, but they inherit the sum of both parents' stat modifiers +1. Like for instance, try to have a marriage partner for your avatar unit. Their child is insanely overpowered. XD
Well, that's it in a nutshell; if you want to learn more about skills, I can create a guide for you! o: