Had finches for 10 years many hatchlings never looked inside...how come you know all about eggs in their nest? Birds don't like when you intervene...they want to be PRIVATE...with you and kids looking in ,,,they probably abandoned the 8 eggs...

So you saw those eggs all this time and just assumed everything would be just great. Well, now you have yourself a problem. Not only with the hatched ones but the others in the eggs. Because each egg is in various stages of development. So what are you going to do, removing say, an egg that is due to hatch tomorrow?  Tell yourself that it's not really a bird in there? What are you going to do with the dying babies that the parents wont feed? As they struggle in there with no one to take care of them.

Instead of entertaining your kids with the lives of living beings please THINK before letting this happen again. Yes this is harsh. So is dying.

Two weeks between clutches?  And in the fall?  Of course she let them die.   It's too late in the season for breeding and they cannot be bred off season and one time after another without consequences.

Please don't breed any more, you obviously do not know what you are doing.   I really do not mean to make you feel bad but those babies died because of your lack of knowledge and the hen is next.   Breeding should only happen in the spring and they should never raise more than two clutches.   The last one hatching around mid June.  Please put them on a strict natural daylight schedule to stop this aberrant breeding behavior.

Well, fall is not so much a matter of temperature but a matter of the number of hours of daylight becoming less and less until we reach the solstice in December when the days start getting longer.    And, if I am not mistaken (I don't have a map of the world in front of me now) India is on the Northern Hemisphere so your days must be getting shorter just like here in the States.  Whether you call it fall or rainy season or whatever is irrelevant.  Are your birds on a strictly natural daylight schedule?  Because that would do the trick.

As to how long between clutches, it all depends on how long you allow the babies to stay with the parents.  I usually leave them in the breeding cage for two to three weeks after they are eating on their own because the father continues to supplement his eating and to discourage the parents from nesting again.  Sometimes it doesn't work and the parents start pulling the feathers out of the babies tails because they want to nest again.  When they do that, I remove the hen from the breeding cage and put her back in the flight cage with nest with fake eggs (if you don't, she will lay).   Personally, I only allow one clutch per pair and I don't even breed every pair every year any more.  I alternate them.   But two clutches is good, not more though.   So, all in all, since the babies hatch until she starts laying again, there is a lapse of about 7 or 8 weeks.