Konrad actually describes the procedure in his Book of Nature (puoch von den naturleichen dingen) in some detail. You put a piece of jet (the "black amber" Konrad refers to) into water for three days and then use that water as a) a remedy for undefined pains during pregnancy and b) as a test of virginity. He actually does say how long it will take until the effects of this drink kick in, I'll just quote the passage (this is right after he introduces the two uses I just mentioned):

welheu junkfraw daz wazzer trinkt ist si noch magt sô geschicht ir nihts ist si aber niht maget sô beprunzt si sich zehant VI,39 (whatever young woman drinks this water, nothing will happen to her if she is a virgin, but if she is not a virgin she will piss herself at once, my translation)

His source for this was most likely Albertus Magnus, who describes the same virginity test in the Liber secretorum and De mineralibus et rebus metallicis (B.ii.). Albertus himself claims Avicenna as his source (which is probably true, but I don't know where exactly Avicenna says this. As Konrad's puoch was at the height of 14th-century medival knowledge, and Avicenna and Albertus among the most respected authorities on medicine, it is safe to assume that there was a general belief in the reliability of this test.

The oldest mention of the use of jet in a virginity test I know of can be found in Pliny's the Elder Naturalis historia (XXXVI, 34), where he claims that its fumes can "detect the state of virginity" (deprendit sonticum morbum et virginitatem suffitus). However, Pliny does not specify how this works exactly.

The link between virginity and urination seen before is probably related to the strange relationship between virgins and water in general that writers have claimed since Classical Antiquity: This probably goes back to the myth of the Vestal Virgin Tucca (for example referenced in Pliny's Nh XXVIII,3 and Augustine's De Civitate Dei X,16), who carried water in a sieve from the river Tiber to the temple of Vesta after being accused of unchastity. This myth had a continuing effect throughout the Middle Ages, establishing the sieve as an attribute of virginity in iconography (one of the more well-known examples, though later, might be George Gower's portrait of Elizabeth I.).

This, and here I return to your question, put the idea that virgins are able to "hold water" (in a general sense) to virgins into the heads of the people. Virgins were rumored to be able to hold water (in the urination sense) for a significantly longer time than non-virgins. Because of this, (supposedly) diuretic drinks were expected to have a much stronger effect on non-virgins than on virgins and would compel them to urinate at once.

Konrad's understanding of virginity was most likely a very technical one: a female is a virgin if she has never had any (vaginal) intercourse. But keep in mind that he was writing an encyclopedia and was, at least as far as the medical parts of the puoch go, not primarily concerned with moral connotations here (at other points in the books, primarily when talking about/to the Virgin Mary, the moral part is much more prominent). Konrad's technical understanding is by far not the only concept of virginity during the Middle Ages and not even necessarily the one people actually administering theste tests were sharing!

Other ways to test virginity were: checking the bedsheets for stains after the wedding night and an examination of the woman by (usually) midwives or older women. (I also once read about some measurements of the body that were taken with a piece of string, which was then cut off at the length measured and put around the woman's neck. If the ends of this piece fit together perfectly, she was a virgin. However, I have never seen this mentioned in an actual primary source, so it may well be a myth).

The only part of your question I can't answer is how frequent these tests actually were before marriage. But maybe someone else will fill that in.