Let me try to answer your questions
The voucher is for anyone staying at a Disney Resort with a tee time at a Disney golf course (the website says "select Disney Resorts")
All of the courses are very nice, I'm sure your brother will just be thrilled that you did this for him and will be wowed by any of the courses
Traveling with golf clubs isn't too bad, except for the new charge for a 2nd checked piece of luggage. As long as that's not a problem, your brother probably has or knows someone that has a hard travel case for clubs. You put the whole golf bag in it and you're set

If he'd rather not bring his clubs, there are clubs available for rent.
Time of day is probably a personal preference. I'm not much of a morning person (neither is DH

) and I hate to spend the extra money that could buy more rounds (of golf or drinks

) so we usually play right around 10am. It's nice when you start and can be quite warm when you finish up

Did make the mistake of playing the walking course Oak Trail at 3pm in August once

May is still nice, not too hot, so I wouldn't worry about playing later in the day. The "beer lady" usually comes around several times, she has beer (obviously) water, soda, lunch/snacks. Make sure that he has cash with him for that.
For more info check out
www.disneygolf.com
Hope that helps