-The expression is still in common use, especially when you wanna end a conversation and express your intention indirectly to the other person. -For example, you're getting tired of talking with your friend on the phone and need to get back to work, then you can say" 时间不早了 and I have to finish my work" or when you're working late at the office and wanna end it, then you speak to your partner " 时间不早了 so I need to go home. Let's continue tomorrow". You would sound more tactful and polite with this expression to suggest your leaving. I hope it makes sense. If you have any more questions, let me know.

yes, now we still use it. you will say it when you want to leave or want to do another thing. sometimes really time's up. sometimes it's really you don't have time to keep doing this, you must have to do another thing. but sometimes, it's just an excuse. so it depends. and yes we use it a lot in our daily life.

时间不早了，时候不早了，不早了

This is the spoken language,you could also say “时候不早了”

This is the spoken language,you could also say “时候不早了”