If you are using 'git merge' then you have to use your own copy of core repo to merge the changes you have made to core.
"handling plugins during upgrades"
Go to moodle's plugin site and look up each plugin acquired from there to see if there is a compat version for destination version.
I used to use moosh to do that, but that seems to be broken now. :|
There is no GUI tool to upgrade plugins the same time as upgrading core. So my method of maddness is to check plugins compat first, if all ok, then upgrade core. Upon first login as an admin, update Notifications if moodle hasn't already figured out I need to upgrade plugins.
When it comes to use the GUI in updating plugins, I don't do them all at once ... a few at a time I found doesn't push server beyond it's limits (which creates even more of a problem).
Last resort ... do the plugins manually ... not using their git repos as there isn't a standard to be followed with addon git repos. Spend more time figuring that out! :|
My 2 cents!
'SoS', Ken