You should never end a sentence with a preposition.
I like to follow this one, but only as a hobby, and not in casual conversation unless I'm talking to another pedant. I do admit that the syntactical knots into which I sometimes need to tie myself in order to avoid the preposition at the end make the sentence harder rather than easier to parse. On the other hand, sometimes prepositions at the end can make sentences harder to understand, in instances where the sentence seems to have a different meaning until you get to the preposition at the end. (I can't think of any examples right now.)
You should never split an infinitive
Agreed, that's just plain random.
Never use the passive voice
I have never heard this from anyone except Microsoft Word Grammar Check.
Don't start sentences with 'but' or 'and' or 'however'.
Now now, here I'm really going to have to disagree with you. "However" is reasonable, but "and" and "but" really belong in the middle of the sentence, not at the beginning. There are exceptional circumstances under which you can break this rule, but they're few and far between.