Does this power supply come with a warranty, and if so, what does the warranty cover?

The power supply comes with a 3 years warranty.

Is this power supply compatible with all types of DIN rails, or are there specific models it fits?

The MDR-20 series can be installed on DIN rail TS-35/7.5 or 15.

The output voltage options available for the MW Mean Well MDR-20-15 power supply are 12V, 15V, 24V, and 5V.

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MW Mean Well Plastic Case MDR-20W-12/15/24/5V Ultra Slim Class I Single Output Industrial DIN Rail AC-DC Power Supply (MDR-20-15)

100% original MDR-20W|(12V 1.67A).(15V 1.34A).(24V 1A).(5V 3A) For Industrial PLC sensor
The MDR-20 series is a stabilized ultra-thin DIN rail type industrial control driver
Can be installed on DIN rail TS-35/7.5 or 15,No load power consumption<0.75W
Short circuit / Overload / Over voltage / Over temperature Protections,3 years warranty
30 years of well-known standard power supply brand, 24 hours fast after-sales support from countries in Asia, Europe and America More than 85% of MW's(MEAN WELL's) products can be shipped within 24 hours, supporting mass wholesale.