What I'm trying to say is that this bird seems to be about 2-3 weeks old. How could somebody have her for awhile?

Someone could have kept her if she fell out of a nest at a younger age and they took her in.

she is not seen today. I will keep watching
Should I stay away from that rescue person?

They don't sound like somebody who particularly needs to be avoided if they're the only one who can help. But it would be better if you could locate a real wildlife rehabilitator in your area. The state fish & game department could probably tell you if there's anyone nearby.

if this is the case, what am I supposed to do if she shows up? I am concerned about her getting no water. Yesterday I gave her a bowl but I doubt she drank any water.

What state are you in again, Chipper? I might be able to find some rehabbers in your area.

The bird is definitely a native mourning dove. Most dove-type birds that are actually allowed in captivity, are actually pigeons, and the two dove species that have been successfully kept in captivity are the diamond dove, and the ringneck dove, and those usually look strange enough to stand out (especially if the ringneck dove has any kind of color mutation, including white, because white pigeons and white doves don't occur naturally).

If anything, you can try having seeds in your hand, and try to see if it will eat from your hand. That will be an indication that the dove is tame. Keep water out there, and see if the dove will eventually drink out of it. Sometimes they won't go towards unfamiliar things until they know it's safe. If she gets enough time to investigate the thing you're using to hold water, she'll eventually realize she can drink out of it.

She looks like she has at least gone through her first molt and have her adult feathers, so she might be older than a few weeks. If she is young though, someone could have found her abandoned at nestling stage, and tried releasing her without proper preparations (trying to cut off contact, getting him used to foraging, etc.).

I sent you a message with my location. Thank you for your help!

definitely should be able to fly, correct?

if this happens, then what do I do?

Indeed, she should be. So she could be wild and sick. If it is tame, you could either take it in and try to teach it to be wild yourself, or hand it to a rehabilitation center to do that process.

I've replied to your message, with a link to the one rehabilitation center I could find. If you can't get to them, or they can't get to you, then they could at least point you to somewhere closer. However, I only suggest contacting them, if you see the dove again, as there might be a chance that you might not.