It is assumed by 東京弁{とうきょうべん} you mean 標準語{ひょうじゅんご} - Japanese Standardised Language. Although there is a dialect called 東京弁 some have argued it contains elements from all the different regional dialects as people have gravitated towards the capital. Further, 東京弁 contains two traditional sub-dialects [山]{やま}の[手]{て}[言葉]{ことば} and 下町言葉{したまちことば} both of which have almost died out (as they were absorbed into the Tokyo standard).
In 標準語 these words do not officially appear (even in spoken examples). However, they do see use especially with younger people and especially with males. Almost all the words you have mentioned sound like they come from a High School to Mid 30 year old male. As to some being "extremely rude", if the initial word before the diphthong edition was rude, the word still retains it's appropriate level of rudeness.
Also to look at some of your examples...
- うるさい may also be heard as うぜえー
- 嫌{きら}い does not become きれえ. Your initial assumption about hearing something else was correct.
- Most often 綺麗{きれい} becomes きれえ.
It is of note that in almost all circumstances using these words will not elicit good responses from people unless you know the person quite well or would like to get into a fight with someone (in the case of referring to anyone as てめえ).
It is most likely to be done to adjectives, but it is difficult to come up with an all encompassing list as this can be done to a great many words. However, here are a few.
As to the productivity of the change, that is largely based on the speakers preference. It is often seen to be easier to speak as this type of language accentuates rolling between syllables without pauses rather than pausing as you would with 標準語。
The rules / exceptions that prevent the change would be that it isn't considered proper Japanese (標準語) nor is it generally considered gender neutral. Also, some perceive people who talk this way as either a bit "wild" or somewhat uneducated.
Choco also provided a link to a list of 横浜弁 (which seems to be similarly in use in Tokyo proper [link also includes 山形弁と鹿児島弁] and is all in Japanese).
