More Chamonix: Skiing vs. Trad Climbing

I have 8 days from may 29-june 5. I am thinking about trad climbing and/or ski mountaineering.

1) That time of year, will the trams be open, and will the famous granite trad routes be accesible? Or only the cragging down in the valleys. If the latter is the case, is there decent trad cragging, or is it all sport?

2) Will Mont Blanc likely be skiable at that time? Is there a particular ski route that is recommended??

3) What is the probability of finding quality climbing partners?

4) If anyone is interested in meeting up, let me know.