I make pickles similarly, but not quite the same way: I usually make half-sours, as even the 5.6% salinity of that recipe would be way too salty for my family's tastes. I boil the brine before using it, letting it cool before adding it to the cucumbers. I use a clear glass jar rather than something opaque like stoneware, which might change the mechanics a bit. The biggest difference, though, is that I add a slice of bread, which really gives the fermentation a head start. Usually, the pickles are ready in two days, three at most. Perhaps it's this shortened time period, but I've never encountered any scum that needs to be skimmed off. Sometimes, if it was a particularly hot day or something, there will be mold, either on the bread or on the liquid; if this happens, the pickles are thrown away — it's just not worth the risk.
That said, scum does not equal mold. If it's anything other than white, and/or if it's fuzzy, it's mold, and I personally would not eat whatever it occurred on, unless of course it was rotten moldy milk blue cheese. If it's really just scum, then it's probably a cosmetic issue: if you don't skim it off, the brine might turn cloudy and unappetizing.
Well, if you really want a "definitive" way to measure when lactic fermentation is complete, you'd have to do a laboratory test directly for residual sugars. Most traditional foods that are lactic-acid fermented don't have enough sugar to reach a final acidity that will self-limit continued fermentation by killing all the bacteria. (Foods with too much sugar also often tend to spontaneously undergo yeast fermentation and lead to alcohol production instead if not monitored.) Given the wide variety of fermentation products that can result from initial ingredients and different fermentation conditions, it's really difficult to come up with some sort of "test strip" or something for residual sugar that is accurate. Home fermenters rarely bother with such things, but large-scale commercial fermentation sometimes tests residual sugar content for batches to ensure shelf-stability.
That said, a specific recipe with specific starting ingredients will often have a target pH range, depending on the quantity of sugar in the ingredients, the amount of salt (which in excess will inhibit further fermentation), desired flavor, etc. The composition of the ingredients will determine the mininum possible pH when fermentation is effectively complete.
The desired pH of lacto-fermented foods can vary anywhere from about 3.0 (even down to ~2.75 for some sweet relishes) to 4.5 (more common in grain-based ferments, or quick-fermented vegetables meant to be used up quickly). To answer the specific question for sauerkraut, I'd say most people would say sauerkraut fermentation is "complete" when a pH of ~3.5 or below is reached (though opinions may vary).
Part of the difficulty in answering the question is that home fermentation is often done with the intention of keeping the food "alive" even when it is consumed, which means fermentation will still be ongoing. In most traditional food cultures around the word, lactic acid fermentation is often deliberately incomplete, only used for a short period to transform an ingredient and then use it within a dish for consumption. This contrasts with much alcohol production, where continued fermentation in your final product can obviously create various difficulties for bottling, proper aging, etc.
And some people just prefer food at various earlier stages in the fermentation process. To take sauerkraut as an example, a pH of 4.0-4.5 will be achieved rather quickly (usually within a few days, depending on temperature, salt content, etc.). Some people prefer the taste of a fresher, crunchier product, and they may only ferment for a few days and then refrigerate to slow down fermentation significantly. Other people like to go much further and will ferment sauerkraut anywhere from a month to several months, again depending on temperature -- to achieve a final pH below 3.5 and even down to ~3.0. Over time, the final product will obviously get more sour, but it will also soften and various nutritional changes will take place. It's all a matter of preference when done at home.
Lastly, in reference to the "lagering" aspect of the question, I think the closest analog in lacto-fermentation is the fact that various processes (and various bacteria) will work better at different temperatures. A higher temperature fermentation, for example, may result in a greater acetic acid component in the final ingredients, enhancing the "sharp" vinegar notes. At lower temperatures other bacteria may become more prominent in the fermentation, and in some temperature ranges enzymes and natural (spoilage) reactions may help to change flavor and texture too. Anyhow, for these reasons, some people prefer to refrigerate fermented foods or hold them for a while at "cold cellar" temperatures to allow these "aging" mechanisms to work as bacteria slow down (analogous to lagering). Whether this is done after fermentation is effectively complete or at an earlier stage when the food is less sour again depends on individual preference.
Best Answer
You need the bible of lacto-fermentation 'the Art of Fermentation' by Sandor Katz.
That aside, the general rule is: if it smells and tastes appetizing then it's fine. If it has green, blue or black 'mold' on it, chuck it out. White is alright. Botulism is actually very rare with fermented vegetables. Fermenting is very safe compared to other preservation methods.
Sometimes I get a yukky whiff at the moment I open a fermenting crock, but then once I put a forkful on a plate for a minute it is fine and yummy. So don't decide in the first few seconds.
The best advice I can give on what are the prime factors for lacto going right (tasty healthy) rather than wrong (slimy inedible waste of food) is: use organic veg so you know the right bacteria is present from the start (or add a coupla organic cabbage leaves, they are foolproof). Also get your salt ratio right in the brine, it kills off the baddies. Consider the texture of your veg. If you are cutting/grating it finely, it will likely ferment hard and fast (the bacteria finds lots of surface area). Ferment theses for a shorter time than chunky or fibrous veg to get good complex flavours. Last tip- invest in a good crock with an airlock 'moat' on it and weights in it. they are pricey but really improve your strike rate a lot.
On flavour: veg that has been fermented 'right' has an unmistakable pickles tang at the start, then a lingering complex savoury musty ending. No matter what veg you use.
Oh, and cucumbers (gherkins) are widely held to be tricky to perfect, especially hard to keep crunchy. Beginners usually steer clear. Good first experiments are carrots, cabbages and cauliflower.