Capacitor question for hardware gurus

[nBit7]

'M' may refer to the tolerance +-20% (which is about normal for electrolytic caps)
Or it may refer to a series.

105 degrees refers to max operating temperature.  The temperature before you kill the dielectric.  It has no relation to operating frequency.

The main parameter that decides the maximum operating frequency is the ESL (Equivalent Series Inductance) which is related to resonant frequency.  This information normally isn't provided for electrolytic caps as they usually not used for high frequency applications.

The parameter for more interest is ESR (Equivalent Series Resistance).  This is the main indicator of performance.  Generally Low ESR is better.  But higher performance brings higher inrush currents so sometimes it can be a bad thing.

Low ESR caps usually have some marking or bright colour (orange yellow) to identify them.

So if it looks like a fairly standard cap (blue or gray colour) replace it with a standard cap.

[nBit7]

Newer generation caps will be physically smaller don't worry.
General purpose caps should be fine for most power supplies.  High performance ones can in some cases cause problems due to higher inrush currents.

[nBit7]

Axial capacitor, 25V, 16uF, 85C. It's about 18mm wide, 40mm long. It has "SAMHWA" on it and "(M)8311". Finally the other side says "NPHF"

Axial are getting harder to get.  I am a little worried by the  "NPHF" the "NP" series of Samhwa cap is a non-polarised cap.
Maybe you should post a picture.  

[nBit7]

Ah-ha!!! Is THIS it??

Yes that should be fine.