Just remember, there ARE no stupid questions, just stupid people asking questions!     Just kidding, there are a whole slew of knowledgeable people that hang out around here waiting to answer your questions. And none of us (with the exception of Doug) have ALWAYS known ALL of these answers!   
ADF stands for Automatic Direction Finder. This instrument is used in conjunction with a ground station, called an NDB(Non-Directional Beacon). The NDB is, very simply, an AM radion station, and you can in fact tune AM radio stations as well, with this instrument. I don't think THAT aspect is programmed into the FS version though. The NDB is an older form of Navigation, and has it's limitations. When you tune in the appropriate station(use map MAP VIEW to find these if you don't have a chart) the ADF needle will point to the appropriate NDB radio station.

A transponder is used by Air Traffic Control to better identify you on Radar. When a code is entered in the Xponder, ATC will see it on there radar as well as your altitude, and in turn "tag" your aircraft with your appropriate information. The transponder has an IDENT button, which makes your Radar signature blink on the controllers screen momentarily. This may be necessary when you are close to several other aircraft, and he needs to figure out which one is you.
...Not quite sure what the MKE button is.............possibly a mike transmit select button, for an a/c with two radios ? ?  Which aircraft do you see this on ?

MKR selects the Marker Beacon functions for voice or MB lights or both. When you have the Marker Beacon selected, as you pass one of these stations, you will see either a Blue,  Yellow, or White light on the panel illuminate, and also receive a morse code tone over the speaker. These are used on instrument approaches to verify extent of forward progress towards the runway, but if you fly to most major airports, line up with a runway and you will hear and see these functions.
DME stands for Distance Measuring Equipment. DME is associated with the VOR, and on MOST  Vor's, when you have the proper frequency set, and are receiving a signal, you will also see a DISTANCE readout. This is the distance, in Nautical miles, to the VOR. VOR's posess what is known as "slant range error", and as you pass over the station, the distance indicated will become unreliable. ie: if you are at 6,000', and directly over a VOR, you will indicate 1mile on the DME.

Hi Slaps... ...!
This subject pops up quite regularly.
Have a read here...>>

http://www.simviation.com/cgi-bin/yabb/YaBB.cgi?board=fs2002;action=display;num=...

It may help a little.

Cheers... ...!

Paul.