monitor

No.

When power is available (regardless of the charge state of your battery) plug it in.

There are three different micro-controllers cooperating to be certain the battery does not overcharge. This is a problem for computers, not for people. You should focus your energy on your important work, not the state of your battery.

you will you use a little more of your battery. the higher the resolution the more it will be, however the brightness on the external monitor will not be a factor. Other than that I dont see a 'bad' performance drop happening.

OS 10.14 has the ability to switch between graphic modes for battery conservation.

see this article

https://support.apple.com/en-us/HT202043

Plug in your MacBook when AC power is available, and use it on batteries when AC power is not available.

If you have AC power to run an external monitor, plug in your MacBook as well.

No. If you are using the computer at your desk with AC power available, use it. If you need portability, use the computer on battery.