'... in a home' is used, but it means 'in a care/nursing/old people's/convalescent home'.
Only if you live permanently at the "home" in question. If you're just in hospital for a short time for treatment, then say "I've been in hospital for a week/month".
Did you notice that Rover already changed "for the last one year"? Re-read post #2.
By "permanently", I mean "permanently"! When people move into a nursing home, they leave their own home/family home and they move all their belongings into the nursing/convalescent home. The expectation is that they will then live there for the rest of their lives.
If you're talking about a normal house, where you live alone or you live with your family, yes. That's what "at home" means - "in the house where I live".
As we've explained, "in a home" suggests some kind of care facility.
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