When you are taking cards on your turn, you can choose to take any of the face-up cards rather than taking one from the deck. Taking a face-up card this way lets you choose what you are getting (as long as the color you want is available).
From the rules:
Draw Train Car Cards – The player may draw 2 Train Car cards. He may take any one of the face-up ...
No, you cannot claim a route longer than the number of plastic trains you have left.
Ticket to Ride Rules
Claim a Route
The player may claim a route on the board by playing a set of Train Car cards
that match the color and length of the route and
then placing one of his colored trains on each space of this route...