When you ask for salt or anything else at the dinner table, it's just 'pass.'
· Could you pass the salt, please?
· Would you please pass me the butter?
You could use 'pass' with 'across' if you needed to specify where.
· When a meal is served family-style, dishes are usually passed around the table, not across the table.
The other verbs all usually have different meanings.
If you pass over something, you don't include it, you skip it, omit it, leave it out. (übergehen)
If you have to hand something over, it's because someone orders you to give it up. (hergeben)
If you hand something out, you give some of it to everyone, distribute it, pass it out. (austeilen)
· The Jewish holiday is called Passover because God passed over the first-born sons of the Israelites, sparing their lives.
· 'Hand over that money!' said the bank robber, pointing a gun at the teller.
· The teacher handed out the test papers at the beginning of class.