As ever, a full circuit diagram would be invaluable - even if to show that there is nothing much more present than has been stated.
VAC = 220V so Vpeak = 220*1.414 =~ 310V.
180V DC/310 =~ 0.58
This is the sine of thge angle when the rectifiers start (or end ) conducting + 35 degrees.
For 35/90 of the cycle the voltage in is below Vdc so the cap MUST provide the motor current. If you do not have any energy storage in inductors then the cap is seeing a ripple current of in the order of the motor current and peak currents will very likely be higher (depending on transformer and wiring resistsance and more.)
As dissipation will be in the order of proportional to current squared you probably have about 10 x rated dissiation due to excess ripple current.
Nichicon are a well respected brand. Chances are the actual ripple current capacity on a genuine Nichicon meets or exceeds specifications. But it is unlikely to exceed it by enough to save you here IF the circuit is as it seems. It is possible that the cap is a counterfeit. This definitely happens and Nichicon are a well enough known brand that people MAY counterfeit them, although I have no specific knowledge of this happening in this case.
UUCAP I know not.
It is not unusual for little known Asian components to not come close to spec sheet claims.
In this case it appears that they exceed the specs handsomely !!!!
I'd not complain!
But do look at the actual ripple current.
A small sense resistor in the cap ground lead will allow a scope to be used with due care (or in the "hot" side with an isolation device AND if you know what you are doing. Or a Hall clamp / proximity meter or ... .
Note that cap lifetime ~+ Rated hours x 2 ^ [(Trated-Trun) / 10 ]
It is usual to run a cap at WELL below rated temperature.
30C below = 2 ^ (30/10) = 8 x rated lifetime.
So a 2000 hour rated cap would last about 2000 x 8 = 16000 hours ~= 2 years.
The larger margin the better.
Note that an Al electrolytic cap with NO applied voltage, held at high temperature will die faster than when voltage is applied !
Generally (not always, due to manufacturing defects) the short lead is the cathode, negative; while the long lead is the anode, positive. When looking at the can, the lead that matches up with the rectangles which are negative signs, is the cathode side.
On SMD aluminum cap cans, the topside marking usually denotes cathode as well. SMD tantalum caps, the line usually marks the anode side.
The absolute best way to tell, is to look at the datasheet and see how they call it out, though the above can be used as a guideline.
It depends, with bypass caps they need to have the same ESR. The other problem is the leads from through hole caps will have more parasitic inductance. So make sure the leads are short, and you match the ESR (or have lower ESR) with the new capacitors.
For capacitors that are connected to filters of DC to DC converters, it's best if all specs are matched exactly and the capacitor is installed in the same manner, even trace size or leads can add parasitics that can cause loss or instability in a DC to DC converter.