Zombies have a rare chance of dropping a carrot (carrots are the seed, no need to make a seed out of a carrot, simply place the carrot itself in the ground) and you can also get carrots from villages. Villages are typically found on flat lands, and finding a village would be easier, unless you have a bunch of zombies around!
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You do not need carrot seeds to plant carrots. If you have just a carrot, you can plant that in hoed land.
There is an infinite amount of seeds in minecraft.
there are about 2^64 18,446,744,073,709,551,616 Minecraft seeds
Minecraft seeds can be found on the Minecraft forum. See the related link below.
Good seeds vary between different Minecraft versions.