Is it possible to use the same payout address on multiple miners at the same time? I just started out mining, and I'm using Nicehash to mine BTC, so my question is if I ran the Nicehash client on two different computers in my house, both using the same wallet address, does it add the profit to the wallet? What are the problems with it if i do use this?
You could use the same address with both miners and there would be no problem. Addresses can be reused, even though this is not recommended due to privacy concerns. 

However, you will never manage to mine any bitcoins with home computers. They're too slow and don't contribute enough proof of work to get paid.