Welcome to the forum.
Location is helpful for any advice here. If you don't want to share your exact state, you can find your USDA plant zone here (if you are in the USA)
https://planthardiness.ars.usda.gov/PHZMWeb/
Just tell people your plant zone and we can help more.
Pics of any tree you have a question about helps as well. So many issues have some of the same symptoms when described, but we have people here that can pick up a ton of nuance to your issues just by seeing a picture.
As far as your initial questions - when a plant grows from a seed, that plant has everything it needs to get started right inside that seed. Depending on how long they have been growing, your plants may still be in this seedling phase. With pines, it will be a small growth of needles, then you'll see the second set of "real" needles growing in - which should be accompanied by some root growth.
It's smart to protect them early from excessive rain, but remember that most pine species need to be out in full sun, so you may be moving that tray in and out of the house until your weather dries out - too little sun and your seedlings will die.
Once they've grown out for a bit and have multiple sets of needles, you can begin trying to identify by counting the needles in each of the sheaths and matching with species. If it's a grow your own kit then your seeds were most likely Japanese black or red pine. Possible Japanese white pine.
Hope that helps.