The first looks like Japanese barberry (Berberis) and the second looks like privet (Ligustrum). Both are invasive (seeding into wild areas) in some parts of the country, but I don't know if they are in Nebraska.

I also think the first one looks like Berberis. Give it a pat. Does it have very thin, sharp spiny thorns that try to take your arm off?

Not sure on second one but yes, privet sounds a distinct possibility. Are the leaves more leathery than the beastly Berberis? The good thing about privet is that it is a friendly thing to remove.

I will check into that invasive issue, thank you for your help!

Also, everything is MUCH too close to the house because the beds are much too shallow front to back.