"wenッ- ン - cheated". Sounds like "wen "chisai tsu", "n" , "cheated"

And therefore, if the weak form of "and" is simply "n" -- as it very often is -- then this lonely "n" sound would be assimilated to the "n" sound at the end of "went" (the T is not typically released after N at the ends of words). Thus "went and cheated" would sound like "wen'ncheated"

I can hear it in the song, but he doesn't clearly pronounce the ending constant so it sounds like "an" instead of "and" "an my girlfriend went and cheated on me"

Sometimes, when a writer is trying to show clearly that "and" is being pronounced in this way, they will write it with apostrophes for the "a" and the "d:" "ham 'n' eggs" for "ham and eggs." That is, apostrophes are used to show that neither the "a" nor the "d" in "and" is being pronounced, but just as if it were a isolated little grunted "n." For example, Mark Twain, in "Roughing It," has a character say: "But if the ground suited him, he would lay low 'n' keep dark till the first pan was washed, 'n' then he would sidle up 'n' take a look..." meaning "But if the ground suited him, he would lay low and keep dark till the first pan was washed, and then he would sidle up and take a look..."

Yes, "and" can be very weakly, almost imperceptibly, pronounced. It is one of a set of words called function words. Function words include conjunctions, articles, pronouns, prepositions, adverbial particles, etc. these words always have a strong pronunciation and also one or more weak pronunciations. A good dictionary, such as Cambridge, will show you both (go to Cambridge's online dictionary and look at the entry for "and"). Weak pronunciations are much more common than strong. I almost never say "and" with a strong pronunciation. This is true in every dialect of English, and it is not informal.