Local car audio stores will usually sell carpet for DIY box builders. Fabric shops might have it. A Lowes/Home Depot might even have it. The cheapest will probably be the internet though. You want a non-backed carpet so its easy to mold to the shape of the box.
The inside seams can be sealed with many things. Caulking, silicone or wood glue are probably the most common materials used.
partsexpress is a great place to get carpet and they'll have it to you in 1 business day since you're in ohio and they are located in Dayton. An audio shop might sell u a 5 yard roll as well for like $20-$30