1. Please try to forget the term "redshirt", or at least recognize it as ill-defined slang. It has no meaning within NCAA rules. In D1, a player gets 5 calendar years in which to use up to 4 seasons of competition. The rule applies to any student, whether on scholarship or not, or even if he never tries to play baseball. If he doesn't compete in a baseball season during any year in college, he doesn't use one of his 4 seasons.
So a player who competes during his first year of college and doesn't compete during his second year has 3 seasons of eligibility left, and 3 calendar years remaining. If he transfers to a D1, and has to sit a year, he won't use a season of eligibility during his 3rd year in college, so at the end of the 3rd year he'll have 3 seasons of competition left, but he can't use all 3 because the 5 year calendar limit will expire in two years.
There is nothing special about a "redshirt". Look at it this way: Most students don't endeavor to play a sport, and they "redshirt" for 4 straight years, leaving college with 4 seasons of competition remaining. As soon as 5 calendar years have elapsed since enrolling full-time in any college, their eligibility has expired. It's the same with baseball players, except that some players do compete, and do use seasons of competition.
2. Yes, typically he can play immediately at any division other than D1. He is also eligible for athletic aid immediately, provided he was academically eligible at his previous school.
3. A D1 transfer may receive athletic aid during his sit out year, subject to conference rules. I don't know how often that occurs in baseball.
As a rough statement, students (they don't have to be players!) may receive athletic aid if they are academically eligible and have seasons of competition left.