When does the 2nd person of a verb conjugate with an e between the stem and ending?

Question

I'm trying to learn how to decline the stem of a verb with or without e in 2nd person of verbs with letters like t, ng, d, s, and ß and I've made some rules based on observations. I have 2 questions.

1. Are there any other rules that will make memorization easier.
2. I have a conflict with 2nd singular t-stem verbs below: See BOTH Präteritum and Präsens singular t-stems.

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Konjunctive II

Never contracts except g which can be either.

ich verbärge
du verbärgest <==
du verbärgst <==
er/sie/es verbärge
wir verbärgen
ihr verbärget <==
ihr verbärgt <==
sie/Sie verbärgen

Präsens

d does not contract

ich unterscheide
du unterscheidest <==
er/sie/es unterscheidet <==
wir unterscheiden
ihr unterscheidet <==
sie/Sie unterscheiden

s contracts

ich beweise
du beweist <==
er/sie/es beweist
wir beweisen
ihr beweist <==
sie/Sie beweisen

ß contracts

ich genieße 
du genießt       <==
er genießt 
wir genießen 
ihr genießt      <== 
sie; Sie genießen

t here contracts in singular, does not contract in plural, Can someone confirm my guess that it contracts because of the ä?

ich berate
du berätst <==
er/sie/es berät
wir beraten
ihr beratet <==
sie/Sie beraten

Here Does not contract

ich beachte
du beachtest <==
er/sie/es beachtet
wir beachten
ihr beachtet <==
sie/Sie beachten

Präteritum

d strong verb is either in singular, not in plural

ich unterschied
(du unterschiedest)
du unterschiedst <==
er/sie/es unterschied
wir unterschieden
ihr unterschiedet <==
sie/Sie unterschieden

ich stand
(du standst)
du standest <==
er/sie/es stand
wir standen
ihr standet <==
sie/Sie standen

d weak verb does not contract, Mixed verbs [a.k.a. irregular weak] contract

ich wendete zu
ich wandte zu
du wendetest zu <==weak
du wandtest zu <==mixed
er/sie/es wendete zu
er/sie/es wandte zu
wir wendeten zu
wir wandten zu
ihr wendetet zu <==weak
ihr wandtet zu <==mixed
sie/Sie wendeten zu
sie/Sie wandten zu

s does NOT contract

ich bewies
du bewiesest <==
er/sie/es bewies
wir bewiesen
ihr bewieset <==
sie/Sie bewiesen

ß 2nd plural does contract, singular can be either

ich veranließ
du veranließest <==
du veranließt <==
er/sie/es veranließ
wir veranließen
ihr veranließt <==
sie/Sie veranließen

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Verbs which replace ß by ss follow ß rules.

ich beschloss
du beschlossest <==
er/sie/es beschloss
wir beschlossen
ihr beschlosst <==
sie/Sie beschlossen

t I have a conflict:
Here does not contract

ich beschnitt
du beschnittest <==
er/sie/es beschnitt
wir beschnitten
ihr beschnittet <==
sie/Sie beschnitten

Here Contracts singular doesn't contract plural:

ich beriet
du berietst <==
er/sie/es beriet
wir berieten
ihr berietet <==
sie/Sie berieten

My question 2: Which is the rule, and which is the exception or do you just memorize every case individually?

Answer 1

1. The simple answer is do not learn by trying to apply rules, but just learn the vocabulary as it is. Often groups of words or parts of words have derived during the ages due various influences, usually just people made it easier to speak or adapted to certain modern styles, but there is no absolute, logically explainable concept behind that, not a one they all follow at once. Though your studies may help you personally as mnemonics for your learned words, if they fit your observations.
2. Memorize every case individually.

Answer 2

Präsens

This is not so much a matter of contraction as of when the "e" is neccessary. It seems that it is only neccessary after "d" and "t". Thus, Du beachtest and Du redest are not the general case but rather the exception. The regular thing to do is not to have an "e":

Legen - Du legst

Loben - Du lobst

Lauschen - Du lauschst

What happens in the examples with "s", "ß" or "z" is that (since double consonants don't actually differ from single consonants in pronunciation in German) the second "s" doesn't get pronounced, and is dropped also in orthography:

Reisen - Du reist

Reißen - Du reißt

Reizen - Du reizt

The only exception to the rule that you get "e" after "d" or "t" is words that show vowel change, as you guessed:

Raten - Du rätst

Werden - Du wirst

The same is true, by the way, for 3rd person -t: It only gets an "e" in between if the stem ends in "d" or "t", but not when there is vowel change:

Beachten - Er/sie/es beachtet

Reden - Er/sie/es redet

But:

Raten - Er/sie/es rät

Werden - Er/sie/es wird

However, as Janka mentions, many words that in written language receive vowel change don't behave that way in spoken language, thus it would be very normal to say "Du ratest". That isn't true of all such words though. E.g. it would be very odd to say "Du werdest" instead of "Du wirst".

Präteritum

I wouldn't worry about the 2nd person forms of the Präteritum, since they are almost never used (Except "du warst"/"ihr wart" and "du wolltest"/"ihr wolltet".) at least where I come from: You don't use them in speaking, because you never use the Präteritum there apart from "war"/"wollte", and you don't use them in writing, because the sort of text where you use the Präteritum is the sort of text where you wouldn't use the 2nd person. I don't know if people from the north use it more though, it seems possible.

As far as I'm aware, you would usually only have the "e" after "t" and "d" again, but even there it isn't obligatory (except in weak verbs where it is always there, that is, verbs that just get the "-te-" to mark the Präteritum). I doubt that "beschnittst" or "berietest" is actually considered wrong, although people would probably not say "beschnittst" since it would sound exactly like "beschnitzt".

Konjunktiv II

I believe in Konjunktiv II, too, the rule is that you have to have the "e" after "d" and "t", but I'm not 100% sure on that. To me, words that don't end with "d" or "t" sound a little odder without "e" than with "e", but then, most verbs sound odd in the Konjunktiv II to begin with.

Should you learn the rules?

I would try to remember what classes of verbs pattern together and then to learn one word that is representative for each class. Then you only need to remember that, say, "reiten" patterns like "beachten", and so on.

Answer 3

The most general rule that I can think of (which probably still has loads of exceptions but at least gets you somewhere) is that contraction occurs if the consonant preceeding (e)st or (e)t is not part of a cluster and that it does not occur if the preceeding consonant is part of a cluster.

For most German speakers (explicitly excluding some southern dialect speakers who have a tendency to allow for consonant clusters), combinations such as *beachtst are very hard to pronounce. In the first person, this verb is be-ach-te (with hyphens here to represent syllable boundaries) so you may notice that the consonant cluster cht belongs to two different syllables. This is true for any form of beachten that has an ending (i.e. it still can be beacht). So however sloppy you may pronounce be-ach-test, it will always be a three-syllable word.

If, on the other hand, you have a single consonant or a combination of approximant and consonant at the end of the stem, German syllable structure allows adding (s)t to the end of that to still give a pronounceable syllable. So for example a shwa in the word beherzt (to make beherzest) is allowed but dropping it still gives a pronounceable syllable. Only here can the tendency to shorten even occur, because beherzest can be shortened into beherzt without turning it into a tongue-twister (as would be the case with beachtst).

The additional rules are such that an s may merge with a following s but there must be a separation between two ts.

However, I would always expect exceptions to these rules (as mentioned at the beginning) just because of the way languages work.