“Has” is used for singular and “have” for plural. “Inmate” is singular, so you use “has”.

This site may help.

The inmates have been — you need a plural here because you can substitute “they”. The inmates have been… they have been. As your sentence reads now, you should say, “The inmate has been” because you can substitute he or she. “She has been,” or “He has been”.

“She has” is correct. “James has” is correct. “They have” is the plural. “She and James have” would also be correct.

Now, besides basic subject/verb agreement, you also need to know how to use plurals when speaking abstractly or in general. The following sentences might help:

The goings-on around here have been strange.

Her philosophies of life are strange.

I hope this helps. Cheers, K (English teacher, 15 years)

So, The inmate HAS been..

The inmateS have been…

The rest of your sentences are correct, as they both only talk about one person.

Does that help?