I am a Computer Science student, and I've transferred to another college that uses an unfamiliar language (java SE). I've read over the stuff at Tutorials Point, but I tend to learn best by doing. I was wondering if anyone has a list of general exercises to test basic knowledge of a language?

For example, something that would take you through stuff like how to handle standard features of programming languages like loops, arrays, functions, classes etc. so that I can be sure I know the proper syntax and anything else that may be different about the language.

My advice would be to just pick up an online course or a book which covers your topics, and if you steam roll through everything you're well on track.

I'm more of a "reference" material type of guy, but check out the following:

Java SE 8 -  https://www.udemy.com/java-tutorial/

Java SE 8 Tutorials: https://docs.oracle.com/javase/tutorial/index.html

For loops, array you will find information here: https://docs.oracle.com/javase/tutorial/java/nutsandbolts/index.html

For classes and methods you will find information here: https://docs.oracle.com/javase/tutorial/java/javaOO/index.html

I'll never be able to give you a complete list of all possible options, so I'll just give you one. You can google for others ...

http://www.codewars.com/

When learning a new language or brushing up on an old one, I tend to re-implement the core algorithms in the tools of the language.  

Typically I implement some core data structures like stacks and queues, some searching and sorting algorithms, and minimal interface to visualize them in progress.

A weekend of that is usually enough to ensure I've got enough of the language to get along with, even if it isn't mastery.

I found a new free course of Java - Codegym. Learning is interactive, interesting and understandable for beginners. Also there is a large community of students who can help you!
https://codegym.cc/quests