Is it too early to apply for a Thai visa for travel in May, and can I extend it upon arrival?

Call or email the thai consulate in Coral Gables and see if they do visa applications by post.

A single entry tourist visa is valid for 90 days from the date it is issued, meaning you have that long to enter thailand and get stamped in for 60 days.

As long as you're entering thailand prior to the "enter before" date on the visa you'll be stamped in for 60 days.

If you're a US citizen you don't need to get a visa for only 60 days. You can come and get a visa on arrival. That will get you 30 days and that can be extended an additional 30 days. The extension cost $60/USD and can be done at the Immigration office. Careful about this - you have to be able to get to the Immigration office 1-14 days before the visa expires. If you plan to stay on a remote island for the entire 60 days - you maybe be better off getting the visa before you come.

As far as boarding airplane with no visa it depends one the airline and how they implement their policies. Some will require you show onward travel (doesn't have to be flight, you can buy bus ticket for $25 online).

Some embassies and consulates will also accept postal applications. Check on their website for more details.

The visa is valid for 3 months from the date of issue. So if you apply now you'll be good to enter Thailand in May.

Why is being in college affecting your visa application timing?

You can ask for the start date to be up to three months later than the day you apply for the visa.