Lemmur adds lemmy.ml by default if you don't have any instances added (otherwise it would just be completely empty). If you go to settings > accounts you can remove any instance by long pressing it.
You cannot react to posts if you are not logged in (otherwise your vote couldn't be synced with lemmy servers). To log in you can visit the same page where instances are. Lemmur "pretends" that you have an account to enable you to browse content without the need of being logged in (anonymous account), of course not everything is possible without being logged in hence some things are inaccessible.
Hope that clears it up and let me know if you need more help
Push is definitely not happening, we decided that notifications will be implemented as periodical checks