See you are progressing all by yourself now. Good. Just a word of caution ... good idea to read the release notes on each version before gitting the code. Why? For the questions you've asked indicate changes have caught you by surprise.
One of the major changes from 2.6.x to 2.7.x IS themes. All the 2.6.x themes not compat with 2.7.x and in 2.7.x you only have two (to start with). When you go to notifications now, check for updates, if you see a link that says something about 'some of your plugins' ... then follow it. Those plugins need updating to a version that is compat with the core version of Moodle. You will see there that the old themes will be deleted from the DB. That's as it should be. To acquire more themes, visit Moodle's https://moodle.org/plugins/.
Also remember you need to pay attention to the version numbers. 2.4 add-ons may not be compatible with your current version. The plugins area of Moodle.org displays version numbers ... pay attention to them and don't try to bludgeon a mod/block/theme tagged as being compat with say 2.4 into your 2.7, 2.8, or something higher.
One of the nice things ... you can update plugins via the Moodle UI now.
And another note: unless you acquired the plugins via git, when one does a git pull, it will update only the core files of Moodle ... not the addons. For that, go to Notifications, click check update, and use the Moodle UI to update plugins.
And, may not make a difference, but one also might loose a tool or two due to changes in code. In 2.6.x you had an Assignments Upgrade Helper in the Site Admin menu. In 2.7 and onwards, you won't. That helper for converting old assignments mod to new assign mod.
Again ... good idea to read the release notes for the version you are heading towards:
https://docs.moodle.org/dev/Releases#Moodle_2.7
https://docs.moodle.org/dev/Moodle_2.7.8_release_notes
And a comment/personal preference: I normally *don't* go after upgrading to anything .0 on a production server. .0 to me is like being an 'omicron tester'. I'd prefer to be close to the leading edge but not on the bleeding edge with a production box. ;)
'spirit of sharing', Ken