When I worked on the teller line I saw and handled many of them every day. The ratio of deposited vs withdrawn, I saw more deposited. I guess that was true for everything in general, always had a lot more "incoming" than "outgoing", except for coins. For my own personal use, I do not use $100's...I do not carry cash in general. I just use a debit card, and get cash out only on an as needed basis.
In regards to counterfeits, I have seen a few... some pretty good, others not at all. Our counting machine would detect counterfeits (well nothing is foolproof). Old bills would always trigger counterfeit on our machine. I would say MOST counterfeits can be spotted fairly easily. First of all, they something just looks "off" about them. Second, they just don't "feel" right. Also there are things that real bills you need to see (like the face) when you hold it at an angle. We also had those pens, but rarely used them. We used that only if we were really scrutinizing a bill. I have seen a counterfeit $5 before. I had to wonder who in the world would risk prison for such a small bill, but it happens.