You can key morphs directly in timeline by selecting geometry. If you want to do multiple morphs at once you can combine them into a single new morph with https://hub.virtamate.com/resources/morph-merger.142/
You will need to do a hard reset or restart after merging the morph for it to show up in your list.
No, both the built in morphs and skins are inaccessible for copyright reasons. Meshed has the right to use the assets in the game, but can't distribute them.