I am concerned about the Transit Visas and other rules regarding my visit to Toronto for a few days, and how frequently I can visit Toronto to see my girlfriend.
As an Indian Citizen, you will need to apply for a Canadian visitor visa. Holding a US F-1 visa does not change this; a Canadian visa is required. A transit visa is also not acceptable, as you are proposing to visit Canada, not pass through it on your way to or from a third country.
When you apply, Canada will consider you for a multiple-entry visa. With a multiple-entry visa, there is no limit to how frequently you can visit, but you will have to convince the authorities at the border each time you enter. They may be suspicious of your intentions if you make repeated long stays or your travel patterns appear inconsistent with being in the US as a student.
With a visa, you have a number of options, including travel by plane (1.5 hour flight), with flights from all New York-area airports, bus (it's a 10+ hour trip), train (12.5 hours), and driving yourself (8.5 hours, plus traffic, stops, and border crossing time).