Hi
Locals do speak Englsih but not much... I guess it depends on where you are. Industries that cater to tourists you'll find a high percentage of english speaking, also younger people are more apt to speak english than older adults. The last time I was there I had a few basic phrases figured out:
Thank you (very much) -- Domo arigato gozaimasu
Excuse me (to get attention) -- Sumi masen
or Excuse me (pardon me) -- Gomen nasai or Shitsurei shimasu
Please (when requesting something) -- Kudasai
Do you speak English? -- Anata wa eigo o hanashimasu ka?
Where is it? -- Doko desu ka?
How much is it? -- Sore wa ikura desu ka?
Since you'll be there for a couple month buy a phrase book.
I didn't see when you'll be traveling so I can't help on the weather.
You might consider renting in a Gaijin house. They are shared houses or apartments where you can stay in a dormitory or have your own room, but bathroom and kitchen facilities are shared. Rent can range from around 50,000 to 100,000 yen per month.
You might have a hard time finding a apartment to rent if its only for two months. Maybe look into a long term hotel. You'll find that Tokyo is expensive but an amazing place to visit/live.
Here's a few
things to do in Tokyo.
Happy travels.