Example #1: Fun fact: If a Trooper (at least in Ohio) tells you that you were speeding or gives you an exact speed you were going, it's in their policy that they have to cite you. If they don't, they get written up by their supervisors. Very well could be you were speeding but he didn't feel like messing with it. Everything they say is recorded.
Example #2: He said you were following too close, you disagreed. His word vs yours.
Example #3: No comments as I don't know many laws and policies in Texas.
I'm not saying cops are perfect. They're far from it. Unfortunately there are those ones out there that give all cops a bad reputation It just gets old seeing people bitch and complain about cops because they got a speeding ticket 5 years ago or some crap like that or they tell a story to make the officers look bad when it was in fact a justified stop.