Getting ones head down could simply be used as meaning to concentrate on a task. Sample sentence, " my exam is coming up next week, it's time for me to get my head down." it is a phrase used both in the UK and the US.

To hit the sack ,go to bed is common in my country. It's such a schlep Yiddish word shchlep for hassle

'Have forty winks' is one of those phrases that always comes up in lists of entertaining English idioms, but I've never heard anyone say it. We'd be more likely to say 'have a nap'. The others are used from time to time. 'Hit the hay' is a variation on 'Hit the sack'. It's not something I'd ever say myself, but the expression exists.

Yes Iris all of these phrases are pretty common.