Chat apps and email cap attachments at sizes a phone video easily beats. The quickest fix is to shrink it to the limit, and you can do that without sending the video anywhere.
Length, picture size and detail decide a video's size. A one minute phone video at 1080p can run to well over 100 MB, and no setting will turn that into 8 MB without giving something up.
The easiest thing to give up is picture size. Going from 1080p to 720p cuts the amount of picture by more than half, and on a phone screen the difference is hard to see. After that, a shorter clip helps more than anything else, so trim the video first if you can.
The size you pick is a target, not a promise. The result usually lands a little under it, but allow some room if a service is strict.
The video is processed inside your browser, not on a fast server. Expect roughly the length of the video for a small picture and longer for HD.
No. It is read and processed on your own device.
Pick a smaller picture size, a lower size limit, or trim the video first.