No, you should never top maple trees. Topping injures the tree and leads to the rapid growth of a weak canopy, which can be hazardous to rooftops and utility lines. Removing the crown can also leave the interior bark vulnerable to sun damage, leading to insects and disease. A topped tree can also reduce property value and permanently damage the appearance of a tree.

The best time to cut down a tree is during its dormant season, typically in winter or early spring, after all the leaves have fallen. Removing a tree during this period is advantageous for several reasons. Frozen ground helps secure the tree stump, protects the surrounding landscape from damage, and reduces the risk of the tree falling in an unintended direction. With the leaves gone, there is less risk of the tree's foliage getting tangled with other trees. Additionally, since this is often a slower season for tree services, you may be able to hire a professional at a lower rate. This dormant period is also the best time for tree trimming.

If tree branches cross well into your property line, in many cases, these branches become part of your property, and you can trim them up until your neighbor’s property line. However, this issue will vary based on local ordinances, so you should do your research before making any decisions. Better yet, speak with your neighbor about how to handle any tree issues. 

If you don’t mind the branches, you can leave them be, but if they’re becoming a hazard, it’s definitely worth having a conversation.

Many species, especially when well-established, are not fans of transplantation. You’ll need to decide if you want to risk splashing the cash, understanding that transplantation isn’t always successful. Again, this is where hiring a pro is helpful, as they can give you all the essential info you need to ensure your tree stands a fighting chance.