Machi Koro Millionaire's Row Moving Company and renovation questions
According to the Note for the Moving Company card in the rules


  The Moving Company can be given to other players


So the answer to the first part of your question is "yes."

The same rules also say 


  The next time a rollwould activate this Establishment and earn income, remove the token instead ...


They go on to give some examples of how card color (activating on your own rolls or other player rolls) behave. In the example you provided, the Corn field would not activate and earn income, therefor the renovation marker remains.

It makes sense if you think of it as the next round of income for the card paying for the required renovations and re-opening the establishment. If it never earns any income, the renovations never happen.