I tend not use the word host in conversation but all of what you said is correct. To host a dinner is to organise and be in charge of the meal, and entertainment. "She makes a lovely host, the meal was delicious and the environment was relaxed and informal. I hope to do this again and I will host the dinner at my home, though I doubt it will be as good as hers."

For the first sentence, I would say "you'd" or "you would" "You could stay for dinner if you'd like." The other ones sound very natural, but "host" sounds like a formal invitation.

@Maria "host" means that you will entertain other people (guests) at your house. @Sinem. The second one (host you at my place) is more appropriate for a formal invitation.

what does " host you at my place" mean?