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This depends on the type of Hajj they are offering. If they are offering tama’tu or Qiran, they must offer sacrifice

This is OK.

His prayer is valid.

It is not permissible to perform Umrah on behalf of the living unless they are not capable. Therefore, if somebody’s illness is permanent , you can perform Umrah on his or her behalf though it is not recommended.

No problem.

There is no limit.

It is permissible to do Umrah and it doesn’t mean that a person is forced to do hajj.

Yes, he can.

No, you can not. You must make your Ihram from Jeddah as long as you intended it from there.

It is not makrooh.