2 - I've got some recording equipment of my own that I bought to make my next CD. Why do I need you?

Simply put, it is the people, not the gear that make recordings great - that really is the critical factor. Great engineers and great musicians have many things in common : years of learning, experience, and practice. I've had many new clients come to me after attempting their first project at home and realizing at the end of the process that their product really didn't stand up to the 'competition'. They did not want to let that happen on their next release.
Think of why you eat at a fine restaurant. You have a kitchen in your home, and all the cooking utensils and appliances you could ever need...but is your output going to match your favorite chef's? The only 'secret ingredient' here is experience. I once heard someone say : "anyone can own a pencil, but not everyone can write like Shakespeare".

3- Don't most studios come with engineers included in the hourly rate?

When you work with someone you have personally hired, you are their priority and their focus for an entire project - not just the next 8 to 12 hours. A staff engineer would generally consider the studio to be his/her priority, which is completely understandable. An independent engineer is also going to be able to give you tremendous help in choosing a studio, and perhaps advising alternate facilities for different stages of a project.
There are other distinct advantages to going with a freelancer working in a room he knows well. The most obvious is preparation. I routinely study charts and demo CDs or attend a rehearsal, even if I am merely recording and not producing a client in order to see what lies ahead musically and how this can best be captured. This does not work as well if I am hearing the song the first time in the studio. Thinking on your feet certainly is a skill you develop in the recording business, but certain possiblities really open up with preparation. One does work differently when familiar with the material and the client 'vision/vibe'.

4- What do you charge?

Please contact me for details.