It’s not legal to intentionally damage a neighbor’s tree. Even if the roots of a tree encroach into your yard, if you damage or kill a tree that belongs to your neighbor, you can be held liable for the damage in most cases. Since herbicides can spread through the tree, causing damage to the whole tree and not just the roots that are on your side of the property line, you shouldn’t poison your neighbor’s tree. The other downside to this method is that if the tree dies, it can fall onto your property and cause more damage, so herbicides are best avoided in this circumstance.

The best way to prevent weeds is to use polymeric sand, which hardens and blocks weed growth when activated with water. If you're using regular sand, you'll need to refill and compact it more often. Keeping the surface clean and free of debris can also help prevent weed seeds from settling in the joints.

Mowing your grass regularly, especially if you’re mowing close to the ground, can help kill Johnsongrass. Frequent mowing helps limit the spread of Johnsongrass and can even deplete carbohydrate reserves in rhizomes over time. The more time you leave in between mowing, the more likely Johnsongrass is to regrow and take over your lawn. 

No, it's not really possible to completely prevent weed growth. Weeds are incredibly resilient—all they usually need is a tiny bit of dirt to sprout, so their eventual appearance is pretty much inevitable. However, you can definitely keep them at bay by getting rid of weeds as soon as you notice them. The longer you let them sit and grow roots, the more they'll spread.