It's very nice of you to do this. Tournament practice rounds are Mon-Wed, tournament rounds are Thu-Sun. Practice rounds tend to be more casual, however among tour players, Woods is especially known for playing as early as humanly possible. Some players will only play a practice round on Tuesday, using Monday & Wednesday to work on the range and/or practice green (there are typically bleachers set up behind the range to watch players hitting shots at the range). Woods WILL play Thursday/Friday (as does everyone in the field) barring injury or a weather delay (they will typically play in light/moderate rain, but if there's lightning anywhere nearby they will wait until it leaves the area); there is a cut on Friday with the top 70 (typically) surviving to play rounds on Saturday and Sunday and anyone outside the top 70 no longer playing for the weekend.
Typically, Sunday tickets are the most expensive as its the final round, but there's no guarantee Woods will make the cut (based on his form you'd think it's a safe bet but at every major there's always a couple guys missing the cut that shock all the pundits).
Neat thing about Bethpage (Black Course) being open to the public is that your brother can play the course and see just how difficult it is, so if you REALLY wanted to be nice you could get him a ticket to a single day AND buy him a round there. Not a lot of major championship courses are open to the public, but Bethpage Black is an exception.