Transport law protection and motor vehicle liability better with different companies?

Hello, I just took out my first KfZ liability insurance. Now I also think about taking out a traffic law protection insurance – 2-3 points I would like to put for discussion, maybe there are already experiences about it. 1. It could theoretically happen already on the first ride an accident etc. and it has been easier, with support in the back – but I have heard that these legal protection insurances often wait for several months i n include contracts, is that right? – are there any companies that offer contracts without waiting time? 2. I mean somewhere to have read that one should take out the traffic protection insurance with another insurance company, than the car liability insurance, because under certain circumstances my traffic protection insurance also has to deal with my own car liability insurance? and there you have better cards when they compete against each other What do you think about this? 3. What else do you consider in the traffic law protection policy? Oh, and what does the abbreviation “TE” mean ? I meet here again and again in the texts …