The number 3 is I guess some sort of SMD capacitor, as shown it's across the two ground planes of the two mosfets.
In circuit it reads 50 ohm and 3xx UF with an LCR meter, out of circuit it reads 10 ohms resistance with a multi-meter and 342 uf with an LCR meter.
Is this normal behavior?
No. With such low resistance the LCR meter capacitance reading is likely to be fairly unreliable.
A similar capacitor on the same board reads 431 nF and does not read any resistance across it like a normal capacitor should.
My questions are:
What type of capacitor is this one?
Probably some type of stacked plastic film capacitor.
Is it supposed to read DC resistance across it's terminals and such a high capacitance in a small package, or has it failed?
No, it has failed. It should not read a low DC resistance. It should indicate infinite resistance on a normal multimeter. A special high resistance meter would indicate maybe thousands of megohms. From the look of the 2nd picture it has severely overheated and the dielectric has partially melted shorting some of the internal plates.
Is it safe to assume it's the same value as the other ones on the board since it's identical in size?
Not entirely safe, but in the absence of any other information it is the best you can do. Best option is to assume it is a nominal 470nF capacitor and scan through catalogs trying to find matching capacitors of the same physical size. If there are several capacitors of the same physical size choose the one with the highest voltage rating.
Can I replace it an SMD tantlum capacitor?
No, a tantalum capacitor would likely burn up pretty quickly in this circuit. The circuit may have a fairly high ripple current through this capacitor and the designer has chosen a low-loss (very low ESR) type of capacitor to minimise the heat dissipated in this capacitor.
Thanks for the reply. Very informative.
I think that this short in the board was due to this particular capacitor shorting which in turn caused those two mosfets to blow not the other way around.
Found someone on taobao selling the board as defective with exactly the same problem, in my case the capacitor looked intact but it's readings was bad, that burning mark in the second photo was while de soldering it. Notice the melted capacitor at the top of the Chinese seller's photo.

According to KEMET and Panasonic datasheets for this type of capacitor and it's size it's supposed to be around 0.39-0.51 UF with a voltage rating of 63-100 VDC and 40-63VAC.
https://eu.mouser.com/datasheet/2/212/1/KEM_F3078_LDE-1103670.pdfI can't find an SMD capacitor with the same shape/type where I live. Can I replace it with a through hole polyester film capacitor like those:

I think manufacturers choose those SMD components to minimize the manufacturing steps, my question is: Does the characteristics of those red capacitors match those of the SMD capacitors? I think I can fit it, and it has the added bonus of being double the voltage rating.
I also found these capacitors which look to be the same type as the original SMD ones but with through hole leads, those are 0.1uF 400V and I think I can fit 2 of those in parallel on the board.

Is that replacement doable at about half the capacitance required?