1. What are you finding "strange"? The spaghetti factory?
2. What is the heating's set temperature?
3. Why do you seem to have so few loops between the joists? I would like to see at least one more loop (that's 4 lengths of tubing, not 2).
4. How is your place heated? Apparently you have 7 circuits (4 going up, 3 going down, I would guess to a basement apartment or similar space) grouped in 3 zones; where are the thermostats for each zone installed? Usually, there is one thermostat and one valve for each zone; I can see the 3 valves feeding each distribution ramp.
5. What kind of surface you have on the other side of the floor? Carpet? Tiles? Hardwood? Laminate? Do you have cracks in the tiles or do you have flooring coming off, mostly the glued one? Is it warm enough during the winter? Is your gas bill high?
Here is what I see: you have a boiler that provides both hot water (the blue heat exchanger) and heating, through the pipes fixed on the back of the sub floor. Usually the radiant heating requires a water temperature in the range of 40-50 C (104 - 122 F) , whereas the water tank requires at least 75 C (167 F). But seeing your coils, I can say that these are too few to be able to heat at lower temperature, so it must be that the water circulating those loops is at higher temperature, therefore your whole system is out of optimum. The high temperature might have a bad effect on tiles (heat stress - cracks) and glued floors coming unglued; the carpet might reduce the heat transfer into your house. There is no 3 way valve for water heating, so the heating and the HW must run at the same temperature; the separation is done by pumps and zone commands. In modern systems, there is a 3 way valve that is switching the boiler, to work on either water heating or house heating but not on both simultaneously; the truth is that the water heating takes about 15% of the time and energy of a house, not long enough for the house to get cold. Your system apparently commands the pumps only, which is not exactly OK because the water will pass through the pumps with relative ease, the stopped circuit acting as a bypass for the active one.
In order to separate the two functions and increase you efficiency, you must install a 3 way valve and the command logic for it; this will allow the two systems to work quasi independent, at different temperatures. To compensate for the lack of coils, you will need to add some radiant surfaces between the joists; simple sheet metal or aluminum sheets will do the trick. Just make sure that the hot pipes are in contact with the metal. This will increase the heat loss/transfer in the pipe, without cranking up the temperature and creating stress in your flooring. Also, the bypass needs a little bit of control; yours is permanent ON and is placed in front of the pumps (as it should, assuming that the feed is up and return down, otherwise it would be even stranger). Your return is sucked with the feed from the boiler, thus limiting the amount of water circulating through the boiler, which is OK if your feed is too hot, but not OK if it's too cold. This impacts on the response time of your heating/hot water system. In a controlled bypass, you will have a valve that is bypassing a low flow restricting element (like a Venturi tube); when the feed water is too hot compared with the set point, the valve will open, allowing the colder return water to be mixed with the hot feed; when the temperature is below the tripping point, the bypass valve is closed and the main flow of water is through boiler, thus transporting the heat more efficiently.
The gray barrel is your expansion vessel. Normally it is installed with the water port pointing downwards, unless the manufacturer is specifying otherwise. Considering the warning label on the tank though, this one appears to be installed right.
The blue box with all the wires coming in is the command unit. This will gather the signal from the thermostats and the water heater and will command the pumps, the zone valves and the boiler ignition according to its logic. It might be a micro controller unit or a CLC/PLC, the end result is the same.