I'm more worried by possible inbreeding in such an uncontrolled environment.
When you only have one aviary, it´s best to buy your birds, and not allow breeding, by means of removing the nest boxes and replacing with shelves, platforms and perches, and removing any eggs laid and replacing with dummy eggs. This way you don´t accidentally have inbred birds.
Those who colony breed, will have various aviaries and log where the birds from which lines go, and move the chicks around to separate them to mix with new blood. As lovebirds mate for life, it´s not common for them to wander off and pair with another bird unless their mate dies.
I would recommend only allowing very few clutches from your bought birds, and when those youngsters go off and find mates, remove their eggs to stop breeding.
Now if it turns out all these eggs are infertile, should I remove them, and will removing them incite the hen to lay again ?
If she is in there, let her sit on the eggs for up to but no more than 21 days. At this point, if she´s still in there, remove the eggs. In a cage set up I´d recommend removing the nestbox too, but I don´t know how that works for aviaries, I´m sorry. Maybe moving the nest box could be an option?
If she abandons the nest before the 21 days, you can remove the eggs after a day or two (to be sure).
she's made a very elaborate nest (whereas the other pair has barely brought in any nesting material), should I leave the nest as is or should I take everything out to let her start over ?
If the nest with the chicks doesn´t have much substrate in, try offering some paper for the adults. It´s important they have enough bedding to prevent splayed legs in the chicks.
When a nest hosts infertile eggs, the amount of bedding doesn´t really matter. When the eggs are removed, the bedding must be removed also.