About the eggs: I would leave the eggs with her for about 21 days and see if she'll lose interest in them on her own without you having to take them. A lot of tiels will lay eggs and if you take them away before they're finished sitting on them (which takes about 21 days) then they will just lay more to replace the ones you've taken, so just let her sit on them for as long as she will or for 21 days and then you could take them.