1) The weather in may is a mixture of rain and sunshine. The warmer days (anything above 24C) are quite humid. Keep an umbrella with you just in case.
2) I wouldn't advise going to the peak on a rainy day in may. It's probably so foggy that you won't see anything.
3) MTR will be much cheaper than taking the shuttle. To plan your trip on the MTR, visit the trip planner on the MTR official website
MTR
4) You can view the Symphony of Lights from the Tsim Sha Tsui Promenade on the Kowloon side of Victoria Harbour.
5) Tsim Sha Tsui has lots of hotels and malls nearby where you could get a good view of the symphony of lights. The best choice is probably the Peninsula Hotel.