Regarding your first point, do you mean that you try running emacs inside a tmux inside a terminal?
If that is the case, I would recommend not doing that. The emacs gui will give you more colours, images, thinner window borders, better keyboard shortcuts (eg a difference between C-m and RET), mouse controls (if you ever want them), as well as potentially less lag.
The analog to the vim-in-tmux workflow is to instead keep emacs always open in the gui, run somewhere between none and all shell commands from emacs (depending on how you feel), and have a terminal in another window (as you might for web browsing or email) for more prolonged terminal things. One might skip this somewhat by running shell (or even term-mode) in emacs.
Similarly, for editing remote files one uses tramp to ssh from inside emacs and edit files whereas with vim one sshes into the remote box and runs vim.
If that is the case, I would recommend not doing that. The emacs gui will give you more colours, images, thinner window borders, better keyboard shortcuts (eg a difference between C-m and RET), mouse controls (if you ever want them), as well as potentially less lag.
The analog to the vim-in-tmux workflow is to instead keep emacs always open in the gui, run somewhere between none and all shell commands from emacs (depending on how you feel), and have a terminal in another window (as you might for web browsing or email) for more prolonged terminal things. One might skip this somewhat by running shell (or even term-mode) in emacs.
Similarly, for editing remote files one uses tramp to ssh from inside emacs and edit files whereas with vim one sshes into the remote box and runs vim.