The cooling system on the 124's is a sealed system i.e. expansion of coolant causes excess to travel to the plastic expansion tank, as system cools down, coolant is drawn back from the expansion tank to keep the radiator full. Here's an explanation of how such a system operates, including the radiator cap, your cap is the type (b) closed construction type in Fig. 5.18 below:-
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Top rad hoses will feel to be under pressure as engine heats up but not excessively so. The rad cap should bleed off excess pressure by opening and allowing some coolant to flow to the expansion tank.
Hoses being sucked flat after a hot engine has cooled down suggests either the recuperation valve in the rad. cap isn't opening (to allow coolant to return from the expansion tank) or there is a blockage in the exp. tank line or tank.
It's also possible that an incorrect rad. cap has been fitted, the cap must incorporate a recuperation valve. The cap opening pressure should be 15 lbs and iirc there are 2 types - long or short, depending on the depth of the filler neck.
For those not familiar with the term 'recuperation valve' - if you look at the bottom of the rad cap i.e. the part that goes into the rad. filler hole, the recuperation valve is a little spring loaded metal disc with it's own rubber seal situated in the centre of the cap main seal. To check if this has stuck, it can be prised open gently using e.g. a small screwdriver, if using a pick, be careful not to damage the rubber seal.
In my experience, the hose/plastic line from the rad. to the expansion tank doesn't usually give trouble but the tank itself can. The hose attaches to a plastic stub on the tank, inside this stub is a metal pipe protruding up into the tank (it reaches approx. 1/2 way up inside the tank, visible with the exp. tank cap removed. This metal pipe has several holes along it's length and it's upper end is swaged closed. This pipe is mild steel and corrodes, badly if system is run without corrosion inhibitors (e.g. no antifreeze or very old a/freeze). This metal pipe, if badly rusted, can prevent the flow of coolant from the radiator to the exp. tank or from the exp. tank back to the rad. This also, could explain the symptoms you experienced with the rad. hoses.
The rad shouldn't need to be topped up in normal use, any topping up is done via the expansion tank, the correct level is the exp. tank is 7 cms above the min. level mark (situated below the mounting strap) on the tank with the system cold. The level will rise as the engine gets hot and may rise noticeably immediately after stopping the engine.
I've never seen one of these Fiats having a water pump with a plastic impeller, they've all been cast metal. It used to be possible to rebuild these pumps,
Fiat supplied a special tool to remove the impeller (it had an internal thread for it's removal), and the seal and bearing with shaft were readily available. (afaik, the same spring-loaded carbon ring seal is used on some other older Fiats and some older Ferrari models).
I'd suggest:-
1) Check rad cap fitted is correct and that recuperation valve is functioning.
2) Check hose/plastic line between rad. and expansion tank is clear of any blockage.
3) Check metal pipe inside exp. tank hasn't become blocked/collapsed.
If this metal pipe is badly rusted (it may even have broken off or been removed) it can be carefully removed from the plastic tank stub and replaced with another pipe, closed off at it's upper end and with a series of holes drilled along it's length - I've used Kunifer (copper/nickel) tubing, iirc it's possibly 8mm outside diameter (early 124 Coupes/Spiders used a much larger pipe on the expansion tank). The metal pipe can also be omitted but it's presence prevents the tank plastic stub collapsing when the hose clip is tightened.
These plastic tanks are usually discoloured internally by rusty coolant - most of this can be removed by removing the tank, inserting some coarse sand + gravel + detergent + water and shaking the tank to remove the rusty stain. This is well worth doing as you can then check the coolant level without removing the cap, + it looks nice.
4) To fill the cooling system, with engine cold, turn heater control on (lever on centre console), remove rad. cap, fill the rad. to the neck, refit rad. cap, fill exp. tank to the correct level (7 cms above the min. mark), start engine and allow to warm up until the rad. fan kicks in while keeping a check on the level in the expansion tank and topping up if the level drops. When finished, refit exp. tank cap. Re-check level in ex. tank when engine has cooled down.
You can if you wish, occasionally squeeze the bottom hose as the engine is warming up and blip the throttle to try to dislodge any air-locks that may be present, but be careful, remember the electric fan may kick in without warning. Don't be surprised if you see the bottom rad. hose collapsing slightly when you blip the throttle as it's on the suction side of the water pump.
I don't think at this stage that there's anything amiss with your thermostat, but you might check that the rad is heating up normally, i.e. cool initially then top of rad. rapidly heats up as thermostat opens (observe water temp. gauge, thermostat should open @ 87*C, 189*F. ). This check is for a thermostat in the cyl. head, if your car has a bypass type thermostat (connected into bottom rad hose) then the procedure for checking may be different?
Afaik, the gauges should all show readings when the ignition is switched on, the engine doesn't have to be running. (the gauges are fed from fuses that are live with ignition on. Maybe someone has been playing around with the wiring? Or was it you who mentioned he had fitted a Lada ignition switch?
There are 2 temp. sender units screwed into the cylinder head, the forward one triggers the high temp. warning light, the rear sender operates the water temp. gauge - earthing the wire to the front sender should light the high temp w/light, earthing the rear sender wire should send the temp gauge to max on scale. Obviously, any chafing of these wires can result in accidental earthing and therefore false high temp. w/light or high gauge readings.
Iirc, on some models, earthing the front sender wire doesn't just light the warning light but also sends the temp. gauge to max on scale - so, if the gauge suddenly reads max, at the same time as the warning light has come on, disconnect the front sender wire and see if temp. gauge drops to normal. (it may be just a failed front sender unit and not an engine overheat situation).