to deal with the loss of reverse 1st
I'm assuming that this is an automatic so I'd take a look at the colour of the transmission oil it should be a dark red colour if its black then its needs changing together with its oil filter. Also check its level with the gearbox warm and just after you've moved the selector through all the positions leaving it for a few seconds in each one and then back to park.
You can top up the box through the dipstick tube if required and make sure you use the correct oil for your car as the fluids are not all the same. Some manufacturers recommended a change of the type of fluid - Speak to the local dealer and parts dept - they will advise you on the updated fluid to use..
If that’s all OK then check all the electrical connections of the gearbox, remove each connector in turn and spray with contact cleaner. Check that the wiring to the gearbox is in good condition with no chafing or frayed wire
If this is OK then check the selector lever linkage / cable under the car for any broken parts and or missing bolts as if this is coming adrift then it can rub on the car body or just bind up
Then - you should top up if low and re try it - or, if its level is ok - and condition is ok - then the next step is to drain it off - open it up and clean the filters inside -- refill and retry it..
that changes things
I'd still check the lever linkage as the 1st step
this will involve getting under the car and examining the gear lever 1st to check for missing bushes and if the anchor point of the lever is not loose
shall I continue or do you still want to quit?
I'll leave you to check the gear linkage to try and remedy the lack of reverse, to address the surging issue
This could be an airleak after the airflow meter, any air dragged in here isn't 'seen' by the ECU and so not compensated for and can lean the engine out causing rough running.
As its a mechanical fault it tends not to turn on the fault light and you can sometimes hear a 'hissing' noise with the engine running.
Check the hose clips for tightness and inspect the trunking for any cracks or splits and also all the vacuum system, the small bore pipes and fittings for cracks and missing parts.
The best way to locate a leak is to have the engine running and warm and then spray lighter gas /propane or brake cleaner around each joint in turn. If the engine rev's up you've found your leak.
Now you might think that spraying lighter gas around a hot engine isn’t wise, however the flash /ignition point of gas is about 400°C so you need a naked flame or spark to set it off and I’ve used this method for many years without incident.
Work your way through each possible joint one at a time and you should find it. I use a slightly flattened piece of brake pipe and some rubber hose from the can of lighter gas to provide a spraying 'wand' and allow a direct blast of gas into each area, especially those difficult to reach with large implements.
It’s also worth getting the fuel pressure checked as if this is low due to a blocked filter or faulty regulator or even a poorly pump will all result in insufficient fuel being delivered to the engine