As a soon-to-be teacher, I am doing a presentation on the laws for public school teachers regarding religious freedom. What are they, and how would one navigate them?

Bottom-line, public-school teachers are agents of the government. As such, they must be perceived as religiously neutral by students. Teachers cannot establish a religion, nor can they inhibit the expression of religion. Having said that, they can openly share about their faith if asked.
You may find helpful information by clicking the “Legal” tab at CEAI's Resource Center.

I don’t require it, but I do recommend that my college students visit my personal website where I post notes and videos for students who miss class to review. As a college professor, is it legal for me to post biblical quotes or religious content on this website?

College students are adults, so you are not at legal risk at this time. However, it might cause a confrontation with the college if someone complains.  If that possibility concerns you, consider creating an “About the Professor” section on your website. Here you can share personal details with your students. You could include a “Favorite Quotes” section where you list not only Bible verses, but some other quotes from secular authors or historical figures (George Washington, Abraham Lincoln, Martin Luther King Jr., or others who often use Scripture in their writings and speeches). You could also include links to your interests, including music, organizations, etc. 

Is it legal for me to make any reference to Christianity (like including a phrase like “Love in Christ” in my email signature and/or posting a Bible verse in my classroom) since I teach in a public school?

Public schools are seen as an extension of the government, so they must remain religiously neutral.
So, including a Christian reference in a school email is not advisable even though it technically is not illegal. While you can use “Love in Christ” in your personal emails, it would not be appropriate for a government agent (a public school teacher) to do so in a government-run email.
However, you can post Bible verses along with other quotes in your classroom. But, if your walls are covered with only Bible verses, you have probably gone too far.
Even though actions such as posting Bible verses in your classroom may not be illegal, they may generate complaints. And your government school must strive for neutrality on religious issues. This may not seem fair and just, but, as a Christian, you and other believers might object to a teacher posting quotes from the Koran in the classroom or putting “Allah is the only true God” in an email.
In the event that your administrators object to your expressions, you must comply with their directives or you may face charges of insubordination. The courts have been clear, your administrators have the authority to control what is put on school walls, what and how you teach, and what is in your school emails.
You can legally live out your faith as a representative of the government in many other effective ways. For more information, check out our Resource Center.  
Contact us at ceai.org/request as specific questions about religion in public schools arise. CEAI is here to serve and assist you to legally function as a missionary in the public schools and to stay employed in the process.

The Fellowship of Christian Athletes (FCA) club at our school has been substantially hindered from publicizing its activities to the student body.
Can public schools set different restrictions for Christian-based school clubs than they do for other school clubs?  

Since the government must remain neutral when it comes to religion, public schools must not censor the private religious speech of students, including the religious messages of student clubs. Therefore, schools must extend equal treatment to all non-curricular clubs, whether they are FCA clubs, Good News Clubs, or Gay-Straight Alliance clubs.  

To submit questions regarding school law issues relating to religious freedoms to experienced attorneys, visit Ask an Attorney on our website. For all other legal inquiries, email service@ceai.org. To submit questions regarding educational issues to our experienced educators, visit Ask an Educator on our website.