If the car has the Autolite/Motorcraft 2 barrel, the fuel filter should be threaded into the carb. Wix #33046.
The loss of performance when applying the brakes, assuming power brakes, points to a bad diaphragm in the booster, a leaking brake booster check valve, or damaged vacuum lines.
You should hunt down the vacuum sources for all of those missing, disconnected or dry-rotted vacuum lines and make sure they are all reattached or plugged off. Vacuum leaks = lean condition, at the very least. If you aren't getting consistent vacuum to the distributor advance (it is vacuum controlled, if still original), the brake booster and the transmission modulator, you won't run smoothly, stop reliably or shift at the proper speeds.
When you think you have all of those handled, get yourself a decent vacuum gauge. At a source off the base of the carb, you should get very close to 22 inches of vacuum at idle.