No reception??

Yes, this is perfectly acceptable. If you are having the ceremony at noon, you will want to make sure you provide a full meal at the church following the ceremony. But there is no need to have a DJ, dancing, etc. On the invitations I would just state food and drinks to follow, or something along those lines.

That IS a wedding reception, and a perfectly appropriate one. The invitation would read no differently. You do not mention what you aren’t offering as a host, only what you are. Luncheon to follow ceremony or similar wording is fine.

Yes, that's a wedding reception, which is hosted food/drink to thank the guests for coming to the ceremony. If you're planning not to serve a meal then have the ceremony at a non-meal time like 2 pm. If you're having sandwiches or something then less need to be concerned about that. The invitations should say "reception to follow" or something like that.

You're basically having a low key reception without the cocktail hour. That is fine. Since it's at noon, just be sure to provide a full meal with seating.

It’s a faux pas to invite people to a ceremony and not provide any refreshments afterwards. Contrary to what social media and Hollywood wants you to believe, a reception can be as simple as a grocery store tiered cake with coffee served at the venue. They are done every day with zero issues. You don’t need a full meal with alcohol or a dj, and many couples don’t have any of those things in sight and they have still properly hosted a reception by serving cake and coffee or punch. That is the acceptable bare minimum even if other posters feel it is inappropriate or inadequate, which it is not.