Firstly, i just want to note that its impossible to be 100% certain of any diagnosis without completing a full hardware test and swapping parts in.

But with this 15" 2011 model having just a notorious graphics fault, i can say that it is nearly certainly a GPU fault with the main logic board.

The 'liquid' or corrosion you see by the Magsafe board and LVDS cable looks more like liquid flux residue, which is used when building the boards. Its typical for the machines that are dropping the components into place to not fully clean this up, but it doesn't cause a problem. But it doesn't look like liquid to me.

The problem with this range was so bad, that Apple actually accepted responsibility for it and did an extended replacement programme for the logic boards that lasted 4 years after the date of purchase.

Unfortunately, Apple never actually solved the problem, so the boards they were fitting as replacements and the same likelihood of reoccurring with the same fault.

The issue is when they swapped to lead free solder for their GPUs, with the aim of being more environmentally friendly. This solder dries out and cracks, causing the GPU to lose contact with the logic board.

Many tried the 'reflow' process of the board, which is only a temporary fix. (this involves heating the board up to 'reflow' the solder under the chip)

The only sure fix is to 'reball' the GPU, which is a complicated process involving removing the current GPU, removing all the solder and replacing it with leaded solder.

We've had a number of these boards repaired by a specialist, and have not had any reoccurrence of the fault. But its not a cheap component level repair to have done.

In essence, if you have the common GPU fault with your logic, you can replace the logic, but it may get the same fault after some time. Or you can sell that machine and upgrade to a later model.

Just to confirm your other question, the Mid 2012 logic board will Not work in the 2011 machine. The are some component similarities, but the display is completely different (the LVDS cable is not interchangeable for starters), so you'll end up sending loads more money buying not only the later logic, but all the other parts that also need replacing to upgrade it for compatibility.

The Mid 2012 model doesn't suffer from the same fault, so i'd class it as the most stable MacBook pro available, and it is the last model before it went retina, so is the most recent and upgradable machine you can buy currently.

Just to confirm my sources, we recycle thousands of Macs a year, and of 188 15" 2011 machines we've recycled in the last few years, i'd say that we've had about a 70-80% failure rate with the GPU fault that apple did an extended exchange programme on. We intentionally dont refurbish this range because of how common the fault is, and we dont sell currently fully working logic boards from this range because of the risk of occurrence and detrimental effect to our warranty service we offer. We pride ourselves on our customer service at TheBookYard, so prefer honesty about the common problems over a quick sale.

I hope this helps.