So I have a paper wallet with BTC (and I assume BCH) that I created before the hard fork. I have recently purchased some BTC and would like to transfer them to my paper wallet. Would this cause any problem or should I create a new BTC paper wallet?
Considering that you are transferring the new purchased BTC to the same paper wallet as you stored the earlier BTC, there won't be a problem at all.
You had 10 BTC before the fork in paper wallet with address 'abcd'
After fork you have 10 BTC in 'abcd' wallet in BTC Chain
And 10 BCC in 'abcd' wallet in BCC Chain
Now you buy 5 BTC after the fork and transfer it to 'abcd' wallet
So, now your final balance will be:
You can use these two balances separately depending on the chain you select.
A wallet can contain multiple addresses. You can transfer new funds to your existing wallet, although the wallet should use a new address for each transaction in order to maximize privacy.
Whether or not you re-use an existing address, there should be no problems using it in transactions after the fork.