Ok, thanks for the extra info.
You would have noticed any warning lights as they would stay on when you are driving.
The transmission's electronic control system relies on many sensors and switches to send signals to the ECM (computer) then the computer in turn shifts the gears. Much of the control system is outside of the transmission.
It sounds like that day in the carpark the automatic transmission was in "limp mode" which gives you 3rd gear only when in drive, that would explain why the car felt heavy to drive, When the ignition is switched off and back on again that resets the system and if the fault is intermittent the light will not come back on and the car will perform properly. The clunking into gear at lower speeds sound to me like a transmission fault as well, possibly one of the electronic controls giving some trouble. The car needs to be connected to a gadget called a Scan Tool to look at what diagnostic trouble codes have been recorded in the car's on board system during the time that the malfunction was occurring. This will enable the mechanic to diagnose the problem and rectify it. The surging at 70km/h could also be related, in any case a trouble code read may help uncover this as well. The brakes grabbing will more than likely be a separate issue but get them to road test the car to see what's happening there. The same thing with the ignition not catching - make sure that you mention that so they can see if there is any codes in the system for that.
Tip: maybe consider taking the car to an automatic transmission specialist.
I would suggest using a member of the Automatic Transmission Rebuilders of Australasia (ATRA). ATRA is a division of the Institute of Automotive Mechanical Engineers (IAME) and brings together a professional highly skilled and dedicated group of Transmission Repairers in Australia and New Zealand. Go to: http://www.atraonline.com.au
& click on member lists to find someone close to you.
Don't forget that if you have any more questions or you are unsure of what I mean in the information provided please ask for more clarification, I'm only too happy to work with you to achieve a good result. Cheers Glenn.