Tree query and weed.?

Hi, hope everyone is well just a quick couple of questions, is this tree ok or should I cut this section out? Not sure what tree it is as my dad planted it years ago every year it gets very rough dark green leaves on it, also is this other plant a weed? I’m guessing it is because it’s spread everywhere. Thank you.

 

I think it is a lime tree. (Not citrus lime!)
The tree looks to be pollarded, athough it may have developed a canker following pruning. Is it in a hedge?, where it may have been topped , and since grown back as a number of shoots. Unless you need to reduce its height, I would probably leave it untouched. If you need to reduce the height, then cut above the head, new shoots will emerge or grow from the stubs. Winter is a good time to do this.More details here:
Pollarding of trees - Basic Agricultural Study

Not sure of the name of the ground cover plant, although its quite common

 

Your weed is probably this.....

Pellitory-of-the-wall | The Wildlife Trusts