Problem: How to recognize and respond to common unfair criticisms made against lgbt people
Recognize what your goals are in addressing these criticisms.
It's a noble goal to want to rid the world of bigotry, but you can't actually change anyone's mind for them. Set the bar too high and you'll probably end up disappointed or burned out.

Answer: An alternative option for a goal would be to let others know that not everyone agrees with messages about lgbt people and they have an ally out there. Another could be to at the very least get a bigoted person to begin to question their views.

Problem: How to cope if you fail your first year at university
Research the best classes available to you.
Go through the course catalogue and make a star next to any classes that get you excited about going back into the classroom. One of the best ways to cope with academic failure is finding classes that you'd really love to take.

Answer: If you can feel jazzed about resuming your studies, even if the subject material might be different from what you studied last year, it'll be easier to move on from previous struggles. Speak to your professors about the courses you found most challenging.

Problem: How to have a relaxing day
Take your time.
You may have a rough idea of what you want to do with your relaxing day. Since it is your day to relax you will want to plan things according to your own schedule without worrying about the usual pressure to get things done.
Answer: Unwind and do things at your own pace during your relaxing day. You may find not having anything planned at all is the most relaxing way to spend your day.