Assigning Current Direction in a Circuit + Resistors
My question is, how do we know which direction to assign them to?


You can pick whichever direction you like. If you're "wrong" then when you solve the circuit you'll just end up with a negative value.


  For example, if resistors are connected like first and second resistors starting from the far left side, are these two resistors in series? 


They're neither. (If you solve the circuit by superposition you might find that for part of the solution they are in series)

Two components are in series if all the current that flows through one must flow through the other.

They're in parallel if the same voltage is applied across them. 

There are lots of ways to combine components that are neither series nor parallel.