Is there a limit to how many free icons I can download?

Yes, there is. If you’re not logged in, you can download up to 5 icons per day. If you sign up for a free account, that limit goes up to 25 per day, which is pretty decent for most small projects.
If you need more, the premium plan gives you unlimited downloads. You can see what’s included in the free and paid versions here: Nowicon Pricing