First off you can candle the eggs to determine if they are fertile. If you see veins then they are. For more info, google search 'candling eggs'.

Now I don't think we can determine why only one hatched. It is possible they were not fertile or that they died before hatching. This could be due to room temperature. They need to be kept warm.

Six is a lot of babies to get in one clutch so my guess is again some are not fertile.

However my expertise is in cockatiels and not lovebirds.

I have 2 lovebirds. One male, One female. The female laid 4 eggs. One of them hatched. It's been almost a month now, and the baby lovebird is doing amazing. However why didn't the other eggs hatch? And now just recently, the female laid 6 eggs. Is there something I am missing? Do I have to keep my room temperature warm or cool? And what else do I need to know? Thanks!