For PSU business travel, am I allowed to buy airfares on the internet? Can I use my brother-in-law's travel agency?

PSU has three contract travel agencies that by contract will give you lowest fares and bill back to your index. If you can find a lower fare by 5%, through any source, document the quotes, book the ticket, pay for it with your Corporate Travel VISA Card or personal fund, and file for reimbursement after trip completion (See travel policy section 405.2).