There are several possible causes for the shuddering /missing which are more likely than the gearbox. (although I m not an expert)Too many to list here really . It may be better to wait until an experienced mechanic can read fault codes rather than wasting time and money hoping to chance upon the cause yourself.
Its possible that a thorough service, changing all spark plugs (some jazz models have 8 spark plugs) would solve the problem, but I mean no insult here, the car is 23 years old with a dodgy gearbox. (and brakes) .
A reputable mechanic would probably assess the overall condition of the car before carrying out any repairs or replacments for any accumulating faults ,rusting , likelihood of its passing its next mot etc .The result may be a recommendation to cut your losses by not throwing good money after bad on expensive repairs or even a service. But some mechanics would just take your money even if the car is a terminal rust bucket. But the car may be sound overall and justifies repairs.
As for binding brakes this can increase fuel consumption considerably, and cause uneven braking, especially if the roads are slippery..The safest answer is to have the brakes serviced/replaced as soon as possible.(subject to my comment above)
However as a short term temporary fix it might help to remove the road wheel and give the brake calipers a thorough wash with a bucket of water with some detergent and a fairly soft wash brush to remove as much road dirt, brake dust etc as you can from around moving parts, sliding pins etc. . You could use a garden hose but beware of using a power washer, or too stiff a brush (and NOT a wire brush) as these can damage rubber seals etc. Then take the car somewhere safe and repeatedly brake much harder than you would normally do to help free up moving parts. There may be no improvement but its free and worth a try. Although modern brake dust is not asbestos try to avoid breathing it in , so wear a face mask, and only use wet wash methods, not air lines etc. Washing it off can cause quite a mess on a driveway so bear this in mind.
