A little help with harmony

I've developed a few assumptions about harmony, I'm not sure if any of them are correct and I wanted to make sure they are before going any further with anything that makes heavy use of it.

* Progressions in major 1sts and perfect 5ths are strong both down and up:

I to VIIm, I to II, I to IV, I to V

5ths are the strongest of the two, and everything else is weak and should as much as possible not be used.

* Dissonent chords add flavor if you get rid of them fast enough with a good resolution

I to VII(diminished) to VI

* There's a technique in jazz and classical music where you sound the chord a semitone away from the one you're trying to get to before moving to it.

I to III to IV

If it acctually exists, what's it called?

* You can put any note on top as long as the bass is either the root note or the third, or the fifth if it's a 6,7,9 etc. chord, anything else would confuse the listener.

* Third and lower intervals have a higher presence in the bass but tend to be a bit heavy on the ear and the lowest two notes in a chord should have an interval of at least a fifth, this doesn't count for diads.

Is that correct?, is there something I'm missing?

Hey sawdust, let me see if I can help you with that.

* There's a technique in jazz and classical music where you sound the chord a semitone away from the one you're trying to get to before moving to it.

I to III to IV

If it acctually exists, what's it called?

First of all, III to IV is a diatonic approach. Considering you are using a major or mixlydian mode, it would be semitonal, but it's still a diatonic approach. There is a technique though, using accidental notes this time, to make an approach by semitones, either using as root the note that is a semitone before, or using the one that is a semitone after the chord you are moving to. If it's a semitone before, you should use a diminished chord as a link between the two diatonic chords. i.e. I - #I

Well, I hope I've been helpful! See you on the forum, cheers!

Acctually you've been very helpful, thanks for that =).