I moved to France from an English-speaking country 2 years ago, with zero French, so I can give you my opinions on this.
1) No, it will not affect your visa process insofar as you can still get the visa, there are not language restrictions on the visa (unless your course is taught in French) etc. However, the administrative bodies (the préfecture, etc) usually do not have people who can speak English running them, so this bit can be complicated and difficult, especially in your first few months, where you have to go to the prefecture to get your titre de sejour. French administration is already complicated and difficult, so yes - this does make it worse.
2) No. I applied from the UK and the forms were in English, although they're usually in French.
3) If people speak English, of course this will help. Your course being in English is vital. But day-to-day life depends where you live. I lived in the suburbs of Paris when I first moved here, and nobody at the supermarket/pharmacy/doctor's office spoke English. I had to get 'supermarket french' rather quickly. If you're in a big city, this is easier, and more people speak English. People will really appreciate if you approach them speaking French, and later ask if they can speak English. In my experience, this makes an enormous difference.
I will say that it's not easy. The French are not known for their patience with foreigners, and even if you do speak French, people won't understand your prononciation and will usually ignore you if you ask them to speak more slowly (in my experience, anyway).
Don't expect your French course to get you up to speed very quickly. Even living here so long, my French isn't great. Especially since I spent a while living in an isolated place.
Prepare yourself to have some difficulty with basic things, like finding a doctor who speaks English, filling in paperwork, going to the prefecture for visa visits etc. When you need to know something about your visa, nobody you can get on the phone will speak English. When you have a problem with your electricity bill, or your phone, or your TV, you will have to get a French-speaker to call for you. In essence, it adds a +1 level of difficulty to everyday life. It is not insurmountable, but it is rather tiring.
1) French class, and then practicing with people. But don't expect it to work straight away. One loses a lot of motivation working/studying full time. Two years in, I can understand written French, and I can understand it spoken most of the time. I still can't speak very well, but I'm trying.
2) Avail yourself of whatever resources are available for foreigners new to France in science, e.g. Science Accueil if you're studying in the south of Paris - they help you open a bank account and find somewhere to live. Also use the International office of your university, who will help you with visa-related stuff.
3) You have a right to bring an interpreter/translator to the prefecture for your appointments, so grab a french friend or colleague.
4) There are facebook groups where people give comprehensive advice about the very complicated visa system in France, and you can find them by typing 'carte de sejour' and finding the relevant groups.
5) ExpatForum's France section really helped me when expats.SE didn't have an answer I needed, and they all speak English.
6) Gather as many of your personal documents as you can, and take them with you. I mean birth certificates especially. Find out how to get another one from abroad later -- they have to be issued within 6 months to be valid. And then you will have to pay a certified translator to translate them.
7) Get a French boyfriend / girlfriend / platonic friend(s) and practice with them.
8) Live in a city where possible. It's less isolating as a person who doesn't have local friends or speak the local language. If you're from India, there are loads of Indian folks around Gare de Nord in Paris, for example. Side note: There are no onion bhaji in all of France :(