Troubling prepositions

[tangelatm]

Hi!
Could you tell me if the underlined preposition is correct:
1."Drop the letter "a" in "are"
What's the difference between
2.I keep on learning myself...
3. I keep learning myself...
Are the folloeing correct
4.We shall be glad to accept your dinner invitation at the Chef's.
5. I look after people who are ill or injured in a hospital.
How should I rephrase the last one so that students don't infer that people are injured in a hospital?
Lots of thanks,
Angela T.

[Tdol]

1 Yes
2 I keep on teaching myself
Invite someone to a place
OK