Trackpad actions without touching it ( moves, clicks, ..)

Sounds like the Trackpad is bad, or possibly the Battery is swelling & pushing against the Trackpad causing the Trackpad to act oddly. If the laptop still has all four of its feet, does the laptop sit firmly on a flat table or desktop or does the laptop wobble a bit which may indicate a swollen battery.

Trackpad failures can be intermittent. I have replaced a lot of Trackpads on our organization's non-Retina MBPro 2012 models for the same type of intermittent issues. You do need to be careful since I have seen these Trackpad failures result in having files & folders opened "automatically" and have them renamed with no human intervention (same can happen to data within any open documents).

You should have Apple or an Apple Authorized Service Provider examine the laptop to provide you with a repair estimate. The 13" non-Retina model still has full Apple hardware support for repairs. The 15" model and the Retina models no longer have hardware support except perhaps for battery replacements.

Check the battery now! Trackpad issues like this can be due to a swelling battery. Left alone, the swelling is strong enough to destroy the computer. You cannot wait to check it.

If the battery looks OK, try an SMC reset: How to reset the SMC of your Mac - Apple Support

I tend to agree a swelling battery. I just had my 13" mid-2012 Unibody MBP battery replaced at an Apple Store, and was a little bit surprised that they would still do it. But the trackpad had a different problem in that I couldn't effectively do a "click" except pressing really hard in a couple of the corners. It was obviously a slightly swollen battery that was pressing against the trackpad to the point where it wouldn't click. But a replaced battery and the problems went away, although the trackpad isn't perfect.

Not sure what's the issue with yours, but certainly a swollen battery has been known to register unwanted "touch" from the digitizer. However, it may not necessarily be fixed by replacing the battery if the trackpad is permanently damaged.

MichaelVN wrote:

SMC reset did not helped, problem was back within several minutes.

Sounds more like it's a bad digitizer in the trackpad. On iPhones and iPads this is commonly called "ghost touch". If that's your issue, the only solution is to replace the whole trackpad.

y_p_w wrote:

Sounds more like it's a bad digitizer in the trackpad. On iPhones and iPads this is commonly called "ghost touch". If that's your issue, the only solution is to replace the whole trackpad.

That is what I was thinking originally as it is very common on the MBPro 2012 non-Retina models, but had to mention the battery possibility too.

HWTech wrote:

y_p_w wrote:

Sounds more like it's a bad digitizer in the trackpad. On iPhones and iPads this is commonly called "ghost touch". If that's your issue, the only solution is to replace the whole trackpad.

That is what I was thinking originally as it is very common on the MBPro 2012 non-Retina models, but had to mention the battery possibility too.

Apple might possibly still be replacing these in some places. I know California is still within the 7 year "vintage" period where they still provide service and parts. It used to be that they only allowed 5-7 year service/parts through AASPs, but now they do that in Apple Stores. If Apple or an AASP won't do it, I don't believe it's a particularly difficult DIY repair.