When selecting variable f, the editor highlights other occurrences of the variable. So far so good, but when trying to add them to the selection list with
You can modify the word_separators option to not include your variable prefix (i.e. $ for PHP) so when you double-click a variable name, it will select $ as well.
This option is located in the file Preferences.sublime-settings in your Default folder. I recommend adding the modified setting to Preferences.sublime-settings in your User folder rather than changing the defaults.
"word_separators": "./\\()\"'-:,.;<>~!@#$%^&*|+=[]{}`~?"
Edit:
Unfortunately, currently there's no way to do a Find & Replace within a certain scope. The issue has been raised here, and you can vote for it as a feature request on Sublime's UserEcho forum.
It's a bug. The post also has the workaround.
Rather than selecting the variable, just put the cursor left to it, and press Ctrl+D. This will also select it, but only other variables (or what the editor recognises as variables, based on word boundaries) on subsequent Ctrl+D presses.