ok, I think its a three stage with DI. If I'm right (and the pictures dont make it quite clear whats attached to what) then you have two prefilters, the RO membrane and then a DI filter. Which is excellent.
I'm going to take a guess that the can on the left (from the front) is 5-micron sediment filter and the can in the middle is activated carbon. The remaining one on the right is the DI resin. The 5-micron filter should appear to be a bit like a tube of high density polystyrene. The carbon will be in a canister with a screw off base if I'm right about this.
Numbedr 2 isn't really a straight pass, when the pressure in the 'bottom' section (refer to diagram) is over 40psi then the top section is turned off so its a presure regulated tap. The idea is that it stops the ball valve at the end or the RO unit in general for having to cope with pressure in excess of 40psi reducing the chance of leaks. Where is the flow regulator on your waste pipe?
Normally the waste pipe wouldn't have a T on it except for the flush system around the regulator.
... number 3 goes through the auto=stop doesn't it... and then the waste or RO... so yes - very strange. Perhaps the last owner got really confused and decided to flog it on ebay so some other mug had to figure it out