If I do not put enough starting points or none at all on a map, but I do have plenty or respawn points, will players spawn on a respawn point at the start of the round?
They will spawn in the respawn points. But it should be noted that for Team games, they might not spawn in advantageous locations... So on anything team based, at least have 2-3 start points so that the teams start in the correct general area.
but if I make the respawn points belong to a certain team and not put starting points down, only that team can spawn on those points at the start, right? Also, if I have respawn points belonging to a certain team set up, and then play a FFA game, can anyone spawn on those points or are they only used in team games?
You are correct on the first point. For the second question, I don't really know. IF anyone has tested that, it would be a good question to get answered.
During FFA, the team assignments are negated. I wouldn't recommend assigning spawn points to teams, though. It could lead to some spawn killing for people that know their way around a map and can memorize general spawn locations. The best thing to do is keep them all neutral and use the respawn areas to designate what parts of the map that you want the teams to spawn in. You can use the priority system to make the game know where you'd prefer them to respawn and assign them to teams. They won't always respawn where you intend depending on the level of inherent danger in the area, but at least you have more options than simply assigning a spawn point to a team. It's less time consuming as well. Image having 50+ spawn points that you have to individually assign to teams. Ugh. As for your starting point question, you should use them. There have been several instances where members ask why they start out of the map, and that can be part of the reason (along with not deleting all of the gametype-specific starting spawns outside of the map's play area). Unless you want all of a team to start in a specific location, you really only need one starting point per team since the rest of them will spawn in the surrounding spawn points. It's also good to keep in mind that spawn points count in the overall item limit, so you want to shoot for quality spots for your respawns, not just quantity.
long answers like that is why you are a loyal squid. i would use respawn areas, they're not as complicated as everyone makes them seem, but make sure that assign them a team, i forgot to once and my map was completely broken.