It depends on which wallet you use.
I think there is no diffrence between sending 1000 satoshi or 1000 bitcoin. Just better to use other cryptocurrencies (if possible) to avoid high transaction fee
Yes for sending around 1000 satoshi the fees will be of around $0.5. I think its a big demerit of bitcoin that we cannot send small payments to someone. Only a few private key wallets allow such small transfers you cant even think of transferring such small amounts on third party wallets.