I live in Virginia and like most people here had no firsthand knowledge of the problems until recently. In January I hunted Coues deer near the border with Mexico.
What I saw surprised me. Two things stood out.
1.) The ranchers in the area were descendants of the original homesteaders. They couldn't be more American. Their ranches are on American soil. Yet these American ranchers had fled their ranches. They didn't leave because of drought or a better job offer in a city. They left because the cartel's presence made it too dangerous to stay. Over 90% of the ranches were unoccupied, except for maybe immigrants passing through and spending the night (or day) in an outbuilding. My personal opinion is that these Americans that own property in America deserve a wall that will give them the protection that they need to move back home.
2.) There was a lot of trash in some areas. Not like dumped trash, but more like things that the immigrants no longer needed as they were passing through. It was mostly discarded water jugs and even torn clothing in some cases. They are only passing through this area and have little to no regard for our laws.
Since buying a farm 14 years ago (in Virginia) I've had trouble with trespassers. I prosecuted a couple that drove on with guns. But trespassers were still a problem until I put up a fence. That's right, a simple 4' woven wire fence. A person could cross it if they wanted to but it stopped almost all of the problems with trespassers.
What would a border wall accomplish? It will make it a lot harder for illegal people to do illegal things in America. Right now the Border Patrol has to use helicopters, drones, remote sensors, trail cams, etc and they have to cover 50 miles or so inside of the border. My friends and I were clearly being observed by Border Patrol's helicopters and drones on several occasions. I think a border wall would make it easier (and less expensive) for the Border Patrol because they would only have to watch the wall and maybe a mile or so inside. I see a cost savings to the US taxpayers.
For the OP's questions about the wall and wildlife: it would be tricky, especially near the Rio Grande. Building a wall would be easy in some areas, difficult in others, and nearly impossible in others. Since the wildlife already depends on the Rio Grande in that area and since the canyons all drain toward the river it would make sense to build ponds inside of the wall. This would solve the water problem for cattle and wildlife. Drains/culverts would have to be built in the wall in to allow water to flow to the Rio Grande. The wall would interfere with the natural travel patterns of wildlife.
Similarly, the fence around my farm restricts wildlife travel. The turkeys walk along the fence because they don't want to fly over it. Even deer walk along it even though they could jump it easily. Black bears rarely cross the fence. Coyotes rarely jump it but will dig under it, which is kind of my point. When a coyote digs under the fence it makes a great place for me to set a snare. I'll usually snare a coyote within 2 days. It's much more effective than hole set traps or any other traps that I've used.
Similarly to me trapping coyotes, the Border Patrol would be more efficient in catching illegal immigrants if there was a border wall.
I think a border wall will allow Border Patrol to do their job more effectively, saving taxpayer dollars. To be clear, I think American should permit new immigrants to our country every day, but should not permit illegal immigrants.