In Elliott’s model, price action moves in two types of waves: impulsive/motive waves and corrective waves on all time scales of trend. The impulsive wave is subdivided into a set of 5 lower degree waves. Waves 1, 3, 5 are smaller impulsive waves and waves 2 and 4 are smaller corrective waves. Similarly, corrective waves are always subdivided into a set of 3 lower degree waves where wave A and C are impulse waves and wave B is a corrective wave. In a bullish market, the impulse waves would be rising in price and the corrective waves would be drops in price. In a bearish market, impulsive and corrective waves work in the opposite direction.
A zig-zag is a three-wave corrective pattern against the major trend which breaks down into a 5-3-5 sequence. Wave B falls short of the beginning of wave A and wave C moves well beyond the end of wave A.
A flat corrective pattern follows a 3-3-5. The regular form of this pattern is that wave B falls to the beginning of wave A and wave C moves to the end of wave A. Irregular forms include waves B and C moving beyond the beginning and end of wave A respectively. Another irregular from is when wave C falls short of the end of wave A.
The triangle corrective pattern usually occurs in the fourth wave or wave B of a corrective pattern. The triangle is formed of 5 waves which can be split into 3 smaller waves.
Wave 2 never retraces 100% of wave 1
Wave 3 cannot be the shortest of impulse waves
There cannot be 5 waves in a corrective wave
There cannot be 3 waves in an impulsive wave
Wave 4 does not overlap with the price territory of wave 1, except in the rare case of a diagonal triangle formation
Waves 2 and 4 usually take alternate forms e.g wave 2 is a simple, wave 4 is a complex one (corrective formations can combine)
Triangle formations usually take form in Wave 4
You see the first corrective pattern labelled 'Expanded Flat'? See there is a-b-c pattern going down, another a-b-c pattern going up, then 1, 2, 3, 4, 5 going down which constitutes the 3-3-5 from the flat corrective pattern explained above. See it?
Then another flat correction happened then a zig-zag happened.. so we have 1,2,3,4,5 then and a,b,c then another 1,2,3,4,5. This constitutes the 5-3-5 for zig zag correction.
In answer to your question - most of the time yes, but we could also have 5 waves up then 5 waves down that form a triangle. Your other question: we can have 5 waves down like in the zig-zag, take the first 1,2,3,4,5.. that follows the same logic.
I'd recommend reading Elliott wave principle by Robert pretcher and aj frost to get a better understanding.