We bought a cup that contains 150-300eggs

Onece it hatch we will realase in my woods to eat other insects

Next time we will buy 4 cups hopefully to get 600-1200eggs that will kill other bugs

Mostly to get rid of Mosquitos

If this happens will this bad for the woods for the animals that live here.

The animals that live in these woods are cats, groundhogs, raccoons, shrews, feild mice, possums, deers, and small birds

Will they be ok if we have like 1,200 praying mantis walking around the woods.

You do not say where you are or what species of mantis you have bought - however this is almost certainly a bad idea if the mantid species is not native to your area.

Basically you should never release captive bought animals outside of their native range. The most likely scenario here is that the animals you release will be ill equiped to survive there and so will die which is not a good outcome. The alternative is that they survive and even become established as a breeding population that causes damage to your local biodiversity - a worse one.

People do release mantids into their gardens as pest control. If the species is native I can see the rationale for this (nier than chemical and they are cool animals to watch). However, I don not think this will effectively reduce insect levels in a large woodland area (and if it did, thre are other questions... why do you thik this is desirable? Is it your woodland?).

Sorry - probably not the anseer you were hoping for but please think carefully about the risk of causing ecosystem damage here.