Sri Lankan here.

1) An accommodation budget of $200/night should guarantee five-star accommodation almost everywhere. Also, 8 days should be more than enough to see all of the places you are interested in. You might want to also consider visiting Sigiriya and/or Anuradhapura.

2) The most flexible option would be to hire a vehicle + driver; the going rate is ~$80/day. Note: this recommendation is based on your accommodation budget!

Trains do work, especially between Colombo and Kandy (~4 hours by road, thanks to horrible traffic, vs. 2.5 hours by train) - BUT if you want to travel comfortably, you'll need to book 1st or 2nd class tickets very early on (it might be too late already).

3) Off the top of my head:

a) Sri Lanka has one of the lowest rates of violent crime in the whole world. However, do beware of petty crime.
b) Most locals are hospitable and will go out of their way to help foreigners (without expecting remuneration!). Exceptions to this general rule: shady characters outside the airport, shady characters in 'touristy' areas, and many taxi and trishaw drivers,
c) Uber is extremely popular in Colombo, and will help avoid your being ripped off (very useful at the airport, especially if the hotel isn't picking you up). Pickme, the local equivalent, is also good, and available in several other cities as well (both Galle and Kandy, I think). Kangaroo Cabs is another alternative - and they allow multi-day car+driver bookings as well, I think.
d) Srilankan Airlines offers free prepaid SIM cards (with voice + data) to all tourists arriving to Sri Lanka, from what I remember. Not sure about other airlines - I think that the SIM cards are provided courtesy of the Sri Lanka Tourism Development Authority, and other airlines might be distributing them as well.