I am trying to extract 60W lightbulb from the spotlight, but have just succeeded in spinning the socket inside the spotlight. I am not sure where I need to go from here :( My only intention was to replace the lightbulb.:)

If it is that stuck, you can try spraying some WD 40 into the socket, hopefully you can hold the socket from spinning with pliers somehow. If not you may need to break the bulb, and use a pair of needle nose, inserted into the bulb base and spread open the pliers to grip inside the bulb base.

WD40 in the socket? I would be very wary of trying this, as WD40 is highly flammable.

The socket is spinning because it has come unscrewed. You can either remove it completely and deal with it that way, or screw it back in and deal with it that way. There's a small phillips head screw that attaches it to a bracket, and a threaded rod with a nut that attaches it to the fitter. You'll have to figure out which one is loose.

PS When it comes to actually removing the end of the bulb, I like the "potato" trick.