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.
Yes you are correct wallets like electrum have the fetcher to set the fees as we wish but the only problem with this method is if you screw up the fees to very low you transaction may be stuck in blockchain for days even weeks...

yes bitcoin has a drawback right now.but when it started or if you go back 4 years earlyer.there you can send small frctons of coins without any problem.
but now it has grownup and creates this problem.