You can try this function:
(defun my/open-files-vert-in-new-frame (file1 file2)
The key is select-frame-set-input-focus which makes subsequent functions operating on windows of the new frame and set input focus on it....
It sounds like you would need a function to run once per server invocation.
You can probably use the information in this post to help you set up a hook that would run a function to set the fonts, and then not run that function for subsequent frames until the next time the server is (re)started.
All you have to do is replace the set-buffer-major-mode call which sets the buffer to a default mode (fundamental mode in this case) with a couple of calls to set the modes you want.
org-mode is a major mode, so you set it by calling the function that implements it, with no arguments, in the buffer whose mode you want to set:
(set-buffer <some buffer>)