One thing the tutorial says to do that doesn't seem very wise is to declare new variables in the tick( ) and render( ) methods that run dozens of times per second. Wouldn't using class level variables in the tick and render functions be faster because the program can skip the creation and deletion of said variables.
That depends on what happens there. If they are primitive types (like int, float, ...) then they will be allocated on the stack. That is extremely fast to do and will most likely be faster than accessing member variables.
If they are new'ed then it will largely depend on what exactly happens inside the allocated object. If the objects can be reasonably recycled (like for example something like a Vector3f) then it's probable having an instance around as a member variable could be faster.
Another thing that I was going to do was encapsulate all of my class level variables. My college professor said it is a good practice and he actually made us do it. Eventually I learned to like the consistency of only using get/set methods when accessing class level variables. However, in game programming, I've had lots of variables so far that are never accessed outside the class. Should I only make get/set methods for variables accessed outside the class? Do get/set methods hurt performance at all?
If you end up with one getter and one setter for each member variable and each of those are just of the form "variable = parameter;"/"return variable;" then you are producing a lot of boiler plate code for nothing. It also means you are not really making yourself independent of the class's internal implementation which is usually the point of getters/mutators.
A decent Java runtime will probably be able to eliminate the getter/setter call during JIT compilation but the underlying problem remains. My personal heuristic would be:
(1) the variable should not be directly writable from outside: having a getter method and no setter function makes sense.
(2) modifying the value also requires changing more state (for example setting a dirty-flag): having a setter makes sense, having a getter is optional depending on the need.
(3) although (2) is currently not an issue it could reasonably become an issue in the future.
As usual, there exist a lot of exceptions and corner cases for these rules. But if you cannot immediately point to one of them before implementing the getter/setters, you should spend a bit of time thinking if you really need it or if it's just a band-aid for an underlying encapsulation problem.