Okay, lets try this again......
"My question is, did I break any law?"
*** Based on the information in your post, no.
"Can I just cut the part of the tree that is hanging over my property?"
*** Yes. Any part of the tree that hangs OVER your property line is yours. You can trim and cut to your hearts content.... AS LONG AS you do not damage or cause harm to the tree. If the tree dies or is damaged by your 'trimming', then you could be liable.
"Do I have to ask their permission first?"
"Also, if I start bending a branch that is on my side of the property, and it breaks off on the part of the tree that is on their side of their property, is that illegal?"
*** Yes. Trim the tree properly. Do NOT just break limbs or branches off as that could damage the tree.... and also extends the 'trimming' beyond your property limit.
"Does the cut have to exactly line up with the boundary between the two properties?"
*** No. You can trim it as close or as far as you want..... as long as the cut is on YOUR property side. Do NOT cut anything on their side of the property line. The minute you reach across that 'imaginary' property line, you are trespassing...... just like them entering your property without your permission.
There are at least 17 lawsuits (!!) filed in various courts, including the US Supreme Court, asking if Obama is a natural born citizen (as req'd by Art II, Sec 1 of the US Constitution).
Why has he spent over $1.7M in legal fees to block disclosure... rather than spend $12 for a VALID birth cert to settle the matter? The 'certificate' he has presented doesn't qualify to get a drivers license, wouldn't allow a child to qualify for Little League, or for a real citizen to get a US passport!