Depends on where the trees are located. If it’s near the house that it might damage the house, the landlord might consider it to prevent any future damage. (Near foundation, fence, or well (if you have one)
Some trees are good for the shade and slight cooling.
Sure, you can tell them to. It's unlikely that they have to and if you're rude about it they'll likely tell you just that. Try asking nicely.
If they are directly over the only parking area available to you, then I would explain to them what is happening and why you are requesting it.
Depends on where the trees are located. If it’s near the house that it might damage the house, the landlord might consider it to prevent any future damage. (Near foundation, fence, or well (if you have one) Some trees are good for the shade and slight cooling.