Baggage carts are lining up directly under the fuselage behind the nose gear.
No, they don't, and nobody ever reported this problem. It's surely a problem of having customized the parking in the wrong way.
I have only noticed this once, i tried to change location of the vehicles but that did not have any effect. JPG attached
With your screenshot is not possible to understand what you changed and what the problem might be, because it doesn't tell what you are editing and all the other positions of the vehicles were.
Try to RESET the parking configuration to default, to Undo all your changes, and see if the problem happens again.
Also, (separate issue) even though the scenery AFCAD parking lists Delta, and the real world airport lists Delta at a particular gate, the program loads JetBlue, swissport or any random livery. Is there any way to manually select a livery?
There's no way to manually select a livery, although it's being considered to be added. However, if you had JetBlue there, it means that both JetBlue and Delta were listed in the parking codes, so both operators had the same score, which means the selection was random between the two. If you want to have only Delta there, you should remove Jetblue from that parking in the AFCAD.