MacBook Pro (late 2011) not really working/very slow

I have a late 2011 MacBook Pro running Mountain Lion (v10.8.5).

The day before yesterday a relatively heavy hip flask fell on my laptop, on the right of the keyboard. I'm not sure if this is relevant to my problem; although there seemed to be no damage to the computer (though a bit of aesthetic damage), about half an hour later I heard a loud-ish sound coming from roughly that area (possibly the DVD drive?). Worried, I did a Time Machine backup, and shortly thereafter the laptop ground to a halt. I restarted, and it took an unusually long time to boot, and was also slow at the login screen (the beachball appeared when I entered the first letter of my password.

I've had problems like this before. Two years ago, basically the exact same thing happened, the outcome being that I was unable to repair the hard drive, and had to reformat (it got to the point where the MacBook would not boot, and I only managed to salvage most of my files by using it in target mode with a PC). I had a thread for that issue here: 2011 MacBook Pro periodically grinds to a halt.

So I was basically resigned to the fact I would have to reformat. There were a few files not in the Time Machine backup that I wanted, so yesterday I tried to copy them. Finder was being phenomenally slow - it took about ten minutes to simply drag and drop an item - and the copying process took about five hours to copy 6GB (or thereabouts). By the end of this process, it was very hot. Both now and at the time of the linked thread we've had pretty hot weather (30ish) - I don't know if this might be a factor. After that I reset the System Management Controller. After the next reboot, it seemed to be working ok for about five minutes, then back to crushing slowness.

I turned the laptop on this morning, and everything seemed to be working fine. I didn't do anything particularly intensive, but I managed to copy another 10GB or so onto my external drive, and performed another Time Machine backup, both in completely normal times. I noticed after the backing up that when I went onto Spotlight, it said 'Indexing: 2 hours remaining' (or words to that effect). I used the laptop for about an hour with no problems, then got a window popping up saying "Your Mac OS X startup disk has no more space available for application memory". I am almost certain that there was at least 30GB free, but I deleted a further 15GB or so just in case. I hadn't been doing anything intensive at this point either. It then started to get slow again. I happened to go on Spotlight, and it said 3 minutes remaining for indexing, so I thought I'd wait until that was done and see if performance was back. Twenty minutes later, it still said 3 minutes remaining, and then changed to 4 minutes remaining. Around this point I tried opening Chrome, and with that the laptop ground to a halt. I rebooted, and it seemed to be ok, but again ground to a halt when I tried to open Chrome. I've rebooted several times since then, and performance has been dire each time. Spotlight hasn't managed to get past "estimating index time" either.

I'm happy to format and restore from a Time Machine backup, but:

What are the proper instructions for this?

Is it possible to update to Yosemite during this process?

Is this problem going to go away, considering that something very similar has happened in the past? How might I resolve it?

I appreciate that that was incredibly long, thanks very much in advance for any help.