How to make my Sheik play faster?

I am no slouch on Sheik. I can 0 to death heavier characters consistently and I have placed fairly well in tournaments. I just don't understand how top players like Mr. R, Vinnie, and Zero consistently get raw grabs without being punish by jabs or other moves. I seem to always lag after grabbing, and also experience lag after moves like my smashes, where these professionals throw out the UpSmash and with minimal lag can roll/spot dodge/hold shield. Any tips to make my gameplay faster would be appreciated, not just these two situations.