Most of the issue are pretty easy to sort out if you have some basic tools.
Not many LBS will be bothered to take any time to try and find out what is wrong, in fact I doubt many LBS will remotely be interested or even have the knowledge to repair the electrics.
1. Electrics; bike taking off on it's own is likely down to a wire break in the throttle wiring. To prove this disconnect the throttle and ride without it for a few days/weeks, if all goes well and no more taking off on it's own buy a new replacement throttle. A continuation check can be carried out on the wiring for someone who knows how and a simple wire repair can be made.
2. The starting and stopping over bumps is likely down to bad battery connection with it sitting in it's receiver, look at the contacts on both parts to see if there is any pitting or discolouration due to the shorting electrical spark caused. Check all wire connectors to then battey and at the controller box.
3 . The chain is probably worn or has a bent damaged link also the chain wheel may have worn teeth. Show us some pics.
Measure the chain with a metal or plastic rule, center to center 10 links should measure no more then 25.6cm or for 15 links no more then 38.3cm if beyond this the chain is too stretched causing jumping.
4. Squeaking brakes is likely contamination or dry brake blocks.
Clean the wheel rim with isopropanol or you can try strong soapy water also do the same with the brake blocks, if the blocks look weathered/dry or split simply replace them.