Yes all 3 can be recruited.
For Betamon I believe you have to catch a certain amount of fish
For the other two you'll first have to do the giant Koromon/Black Agumon quest line and then the requirements are below.
Nanimon: 5K wins and all challenges completed
Meramon: Clear Fire Mastery : Endurance I and II challenge
Sounds like you haven’t finished that quest… the discord group has a lot of tips and guides for all the various quests I’d recommend joining if you need help since most don’t really tell you how to complete them even I can’t remember 100% but I will try, I think at the part you’re at you need to talk to some of the digimon in the village who mention him training hard then find him again in the sewers (I think) where you fight again.
Story spoilers below:
After you beat Black Agumon again he gets mad runs off, talk to the villagers again who will mention he has turned into a black Metalgreymon and is attacking people then he attacks Server City (which is a big town), you are asked to go save the city which after you do it unlocks and you can start fixing buildings and recruiting a lot more Digimon including Meramon.
