Many TextMate users have long left TextMate, in fact. So, I'm not sure if it is time to move to TextMate.
Emacs and Vim do what they want, and more. If you can afford a learning curve, it's definitely worth it.
Regarding your question:
View 2 text boxes side by side
You can have two or more windows for the same document. Assuming you are in a "project", right-click your file in the box and select "foo.ext" in the window that opens. The two “views” of content are more or less synchronized, but cool things like editing columns tend to disrupt synchronization.
Due to the way Mac OS X manages windows, a new window is likely to be too large / too small and / or placed in a less useful place. I use ShiftIt to control my windows, in which case they are the same size side by side.
Double-click on the variable and select all instances.
What are you using this for? Is this a visual highlight or non-contiguous choice?
Type ctrl w to select a word, then ⌘ e to make the word a search term, then ⇧ ⌘ f or Change> Find> Find in project ... This will show all instances of the search query in another window. Then you can “jump” to any place and do whatever you want.
If you only want to move from appearance to the place of occurrence, select the word, then enter ⌘ e , then ⌘ g to go to the next introduction.
Another way is to type ctrl s , a small text box will appear at the bottom of the window where you can enter a word and see its first appearance, selected in real time. Re-typing ctrl s will cycle through the entries.
Drag the file to another open window
You can drag the file onto the TextMate icon in the Dock. You can also right-click the file and select "Open with TextMate *" or "Open with ...". If you are in a "project", you can right-click and select "Add existing files ...". Opening multiple files in TextMate will automatically create a “project” for you.