Gaumukh,Tapovan in May/June

himadventures

Yes- you should have all infrastructure besides a good guide.
This place has seen lot of drama when fog comes or weather becomes unstable which is common feature of this area.

You can take take 6 hrs from Gaumukh to Topoban but some have done in 3 hrs also. Walk slow...always !!

himadventures

Yes- you need all infrastructure for this trek. You can estmate a walk of more than 10 hrs from Gangotri. This is long one...i do not suggest to do this.

Take a good guide who can handle situations.Temp. is always hanky panky thing to commit but be prepared for minus 4 in bad weather. This is rough guess.

kolobar

I did it in 2 days one way to Tapovan and return in a day to Gangotri. I was well acclimatized from before but if you are not you should probably take some time - Tapovan is about 4.500m. I did not bring any food nor tent, just warm sleeping bag&warm clothes - Tapovan is a very cold place! There are plenty of dhabas and ashrams on the way for food&accomodation until Gaumukh. I went alone since there is practically a cue of pilgrims all the way. Many continue to Tapovan so you just follow other peoples steps - no need for the guide.
In Tapovan I stayed at Shimla Baba ashram. It is said that he does not accept everybody but I did not see anyone being refused a stay. He gives you a place to sleep and cooks food for a donation.