Is there some kind of display that will show you your signal strength. The speed may not actually increase if you already have a very strong signal.
When you have equipment that has TS9 connectors generally these are for LTE radio. There is a tiny chance they are for WIFI which is used to talk between the device and your PC. If it is wifi then you will get no better signal to the cell tower.
It depends on how they implemented the plugs. They could disconnect the internal antenna when anything is plugged in or they could just connect both sets of antenna. Just because of how radio works it will get the signal over the better antenna even with the others connected.
In any case this is not a software thing. It tends to be a...