When traveling, are you able to start a trip at a transfer?
Actually, Butterflywings’ answer is not correct if you are considering a train journey in the UK (though from the spelling of ‘traveling’ I assume the questioner is in the US). In the UK it is possible with our complex fare system for journeys to more distant stations to cost less than journeys to nearer stations - an example given publicity some time ago was that London to Chester costs more than to the next stations beyond Chester, Shotton and Flint. This is because fares are set depending on size of the market and time of day, rather than just on distance travelled. In this case, if you “travel short” you could be considered not to have a valid ticket, and have to buy a new ticket for the whole actual journey made.
It depends what kind of ticket you have, and which railway. You have not even stated which country you are in.
That's totally fine . The only thing that could happen is, that if the next station is a busy one you could miss out on somewhere to sit. If the first station is less busy it could be more practical to catch the train there. But if the next station is not busy you can board it without any hassles. You have bought a ticket for the whole way. So every stop from the starting point is included in your ticket .