nerdtree auto focus to file when opened in new tab

You can use so-called autocommands, like:

  au BufNew * <command>

It will execute command when new buffer is created. Start from there. Check out vimdoc on the subject.

When vim starts, it opens a window for the file, then it opens another window for NerdTree.

The easiest way to come back to the main window is just to jump to the previous window like this:

" Start NERDTree
autocmd VimEnter * NERDTree
" Go to previous (last accessed) window.
autocmd VimEnter * wincmd p