What could have caused the poor results?
How much time you got? There are hundreds of things that *could* cause an apparently sluggish fermentation. One issue is the low fermentation temperature you described; 40 to 64F, too cold for most ale yeasts.
However, my first question is, "Did you use a bucket for fermentation?" Some of your description suggests that you did and those things are notorious for leaking around the lid seal. Basically, fermentation happened, but wasn't vigorous enough to bubble the airlock because the CO2 escaped through the lid seal.
I added some half of a sachet of another yeast I had in my fridge (again, just threw it directly in the fermenter).
Once a yeast packet is open, use all the yeast. It doesn't get any better with storage. A sealed package is sanitary, but once opened, all bets are off.
Then I bought a bread and pizza dough yeast, but this time I let it hydrate for about 15 min before putting it in the fermenter. Still nothing.
Probably a lot of something, I would think. Most bread yeasts have enzymes that'll break down starches and complex sugars that beer yeast can't touch. Bread yeasts tend to activate in minutes and work quickly.
...during all these actions I was tasting the beer, and realized some attenuation.
I bought a refractometer and noticed that after almost a month of "fermenting", the scale read 7 Brix.
Opening the fermenter and fondling the beer should be a crime. It traumatizes the beer and wrecks your plans for the evening as you wonder if you'll get away with it.
I decided to open the fermenter and give it a stir, and found a layer of mold. That white, bubbly, silky one.
Don't fondle the beer! I don't think what you saw was mold. Aerobic molds don't like active fermentation and almost never happen in beer. That was probably a pellicle, which is a white or off white, sticky and often gummy cover on top of the beer. It's formed by some yeasts and many bacteria as a barrier against other microbes falling into the beer. A lot of brewers see pellicles form when making sour or wild beers.
It could've come from the bread yeast (but likely not) or it could be a sign of other contamination. On the plus side, left alone for a year or two and it could turn into a very lovely sour ale of some kind. Or it could become a lifetime supply of malt vinegar. It's a win-win, if you really like fish.
The fact is: after 10 days of carbonation I opened one bottle and poured it in a glass. The head had a great creamy look, but it didn't last long, fading completely after a minute or two. Regarding the taste, it was watery (maybe a little bit like the Belgian Kwak), and tasted a lot like yeast - maybe because I used 3.5 times more yeast than needed.
Again, keep it in a cool, dark place and just let it sit for a year, then try it.
Try again and use a fresh packet of yeast. Not rehydrating isn't totally bad, but it can cause a 50% mortality rate from the osmotic pressure of the wort. Then, keep the fermentation temperature between 66 and 74F.
Finally, just look for a krausen ring above the liquid line. This is a sign of healthy fermentation. There is no need to fondle the beer.
