The chords of the major scale are I ii iii IV V vi viio (Upper case = Major; Lower case = minor; Lower case with o = diminished).
Each one of those chords has a certain tension - ranging from none (I) to very tense (viio). That tension depends on the notes of the chord (how many notes it shares with the I chord and whether or not it has a leading tone):
- I consists of 1-3-5, and is the most stable chord.
- ii consists of 2-4-6: No notes in common with I, doesn't have a
- iii consists of 3-5-7: 2 notes in common with I, has a leading
- IV consists of 1-4-6: 1 note in common with I, doesn't have a
- V consists of 2-5-7: 1 note in common with I, has a leading tone.
- vi consists of 1-3-6: 2 notes in common with I, doesn't have a
- viio consists of 2-4-7: No notes in common with I, has a leading
There are also differences based on which notes are in the chord, as 1 is more stable than 5, 3 and 5 want to move to 1 but are stable, 2 and 7 want to move to 1 and are unstable, 4 wants to move to 3, and 6 wants to move to 5, but those differences are subtle, so we won't discuss them - just be aware that they are a thing.
We could also categorize those chords into 3 different groups based on their tension: Tonic (stable), Subdominant (some tension, doesn't have a real strong sense of resolution when resolved) and Dominant (tense, has a strong sense of resolution when resolved. I iii and vi are T, ii and IV are SD and V and viio are D.
In functional harmony, T can move to SD or D, SD can move to T or D, and D can move to T. So in all of those progressions, we can see that kind of movement:
- I-IV-V = T-SD-D
- I-iii-IV-V = T-T-SD-D
- I-ii-V-I = T-SD-D-T
- I-IV-ii-V-I = T-SD-SD-D-T
- I-vi-ii-V-I = T-T-SD-D-T
- I-iii-vi-ii-V-I = T-T-T-SD-D-T
And for your other question - There isn't a rule about how long a chord should last, it can last a beat, half a beat, 4 beats and so on... But mostly when talking about pop songs which are usually going to be in 4/4, it will probably last 4 beats (a measure).