The way I score it an infantry division is about 12K with 3 regiments of infantry each. So maybe around 20,000 today.
No the official definition of a US Division is comprised of three brigades or up to possibly 4 and are not regiments. Each brigade is from 5 to 6000+ or up to 9000+ each. They are further subdivided into battalions then companies! Done lots or work in Army and Marine Corps so I know. There is a big unit which is used alot today called a Armored Calvary Regiment which can operate independently or as another brigade with a division.