First to answer some of your questions.
2, you can only set up connection using ttyUSB2 or ttyUSB3. When you set up LTE connection using ttyUSB3, you should use ttyUSB2 to send AT commands. When you use ttyUSB2 for connection, send AT command using ttyUSB3.
3, you cannot use ttyUSB4. It is for other purpose.
7, the log shows 3g should be OK. It does not mean that you only have 3G connection. It is just what the program using compatible protocols.
For 1, 4, 5, this should related to your carrier. Can you try changing TTL like post below. For 6, I am not sure. But seems it is related to 1, 4 and 5 as well.