noobie question about abyssal space

i havent touched eve in forever. and i was going to attempt that new (to me new) abyssal space sites. after test running fits on test server i was going to jump into a tier 4 when i read that you can get flagged for pvp after you exit

whats up with that? if i do an abyssal site in a safe spot or an empty system will people be able to warp to my location or do they have to scan me out first?

do abyssal sites appear on overview to other players?

thanks