Wand and use of magic questions

I must first state that I have not read the books yet. I plan to listen to the audio book while traveling for work.

My first question is about acquiring a wand. Is there an age requirement? Do you have to be a student in order to purchase one as a child? Would a Muggle parent be able to cast a spell using their child's wand? Can you purchase a wand if you're being homeschooled by your parents? Fred and Gorge continue to use/perform magic after leaving Hogwarts (I don't believe they "graduated" unless I have missed that detail). So what/how is use of magic controlled or monitored for adults? If at all?

Second is, I know it's forbidden to use magic up until a certain age (outside of Hogwarts) but we see Harry practicing spells, and the professors tell them to practice between years. Is this more of a dialect issue of the difference between "use" magic and "practice" magic? Or are there certain spells that the professors/Hogwarts/the MoM allow?