Overflow bottle of some kind is very important, as the cooling system needs to stay full of water, with no air inclusion. So when the system warms up, the water expands, exceeds the pressure of the radiator cap (normally 13psi) and the water flows to the overflow bottle. When you turn the car off and the water cools, it creates negative pressure in the cooling system, and sucks the water back down through a valve in the radiator cap.
Apart from that, the conversion looks neat enough. If you're unsure of where those Tee'd lines go to, trace them to their termination and take some pics. normally there'll be an inlet and an outlet from the TB for the cold idle etc, and that looks like where those lines would go. Does the heater work? All the heater lines connected?
Where the thermostat comes from makes no difference, as long as the temp is OK (and they pretty much all are, most cooling systems operate at the same temp). On the other hand, if it's installed wrong, it can cause overheating, but if the car doesn't overheat, it's working. Having it in the top hose is pretty normal too, but it might not be normal for that motor.
That said, 20min to warm up is an awfully long time, does it get to mid-way quickly and hold, then slowly get hot? If that's the case, the rradiator might need flushing, but if it goes straight to 3/4 and stays there, I'd get an aftermarket temp gauge (or borrow one) and find out what it really runs at, because factory gauges can be inaccurate.
-RM.
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