If I have a paper wallet that has .001 btc, could this be worthless in the future because when I sweep the funds the fee is so high?
There's nothing impossible with what you hodl when it comes to bitcoin, maybe over time when the bitcoin market would have surge higher than expected, it would have worth more amount than you left there, you may also make some additional deposits to be able to withdraw or send them together after you would have been using it
How about if I have a paper wallet with .005 btc, assuming it was funded with 5 separate transactions of .001
They don't make deposit or withdrawal charges like the banks do when using a bitcoin wallet, you would have known the rate you will be charged as transaction fee before making the transaction,