Hi there. I am taking my first trip to Zermatt arriving on 13th Feb for long weekend of skiing. I am travelling solo and wondering if anyone has any suggestions for good places to drink and eat (on and off the slopes) or ski runs not to miss (I only have 3 full ski days). Also wondering if there are any organised ski groups or things like that?

The bar at the Alex Hotel is amazing for a nice cold cocktail in front of the fire...

If you've got some cash to burn (around 200 chuffs) I think then get a seat on a helicopter from Air Zermatt to Monte Rosa first thing and cut out the long cable car/chair/poma ride to the top - and it also means you can ski the Cervinia side in the sunshine all morning.

I recommend the sausages and polenta at Monte Rosa Hut. Alternatively theTheodulpass restaurant is very good. If you do go down into the Italian side you MUST try their hot chocolate - rich, dark and smooth, have never seen its like anywhere else.

Now that is a hugely broad question to ask, the choices you have!
Well firstly it obviously matters on how much you are willing to spend, Zermatt isn't the cheapest place on the planet so you will be looking at spend quite a bit if you are looking on going out on and off the piste.
On the Piste: Personally if you have a big of a large budget then i would throughly recommend The Rifflealp Hotel, sadly they have built a new section onto the side of the restaurant so you can;t see the Matterhorn properly but the food in good. If you are really in the mood for a treat and also if you can get in (it gets very busy) is a place just below Furi called Zum Zee. It is truly one of the best places you can eat in the whole of Zermatt but as you can probably guess its not cheap! If you do go get the lamb its one of the best!
Off the slope: In the evening there are some great places to go, if you have just finished skiing for teh day and want to have some Apres Ski then i would recommend going to The Hennu Stall, its got live music everyday and its got some great drinks and is very lively! Get some of the Toffee Vodka!
Hope this helps!
G