You have put a lot of thought into this and have come up with good questions. I sense from your line of questioning that you will do well because you are thinking things through very carefully... Best wishes!!
As a business owner myself, I would first consult a reputable CPA and legal attorney. I know it is some upfront expenses but the last thing you need is issues with IRS, etc. We set our company up as a LLC, I file quarterly reports with the IRS and TWC (TX Workforce -- unemployment fund), process payroll (just the 3 of us--- hubby, me, daughter) and monthly payroll taxes among a lot of other things.
I would set up a separate business because you need to keep personal and business separate. I use Quickbooks Pro 2013 for all of my bookkeeping. It is easy to use. I do subscribe to the program to keep my payroll, etc updated and I process payroll through QB and pay the taxes through it as well. Easy to do.
Yes you need a tax number, state sales and use permit, W-9. The government keeps track of everything we do. We have to show the W-9 to our vendors. We are in raw materials therefore the end user is the one who pays the actual tax on the product but we still have to submit reports even though we do not collect or pay tax on our materials.
I run weekly expense reports which include airfare, personal mileage, hotels, rental cars, webpage charges, entertainment, supplies, etc. I'm probably considered OCD when it comes to my detail with my company as far as receipts, and to the penny reconciliations,etc. You can run your business cards through the expense reporting... we get ours at staples and 100 cards are about $30. We pay $14 a month for our website.
Depending on how large and busy you get.... you have options for other things such as fully finding medical coverage and 401K's. Our company pays 100 of the medical and we have 401K's set up as well. Of course this is not something you have to do from day 1 or at all if you intend to be more personalized and keep your business relatively small.
I don't know any details regarding liability insurance. You might ask the CPA, attorney or your insurance agent about that. Our insurance is based on our materials in case they are damaged in transit, wrong formulation, etc.
Bottom line, I would set this up as a separate business and then you go from there with the growth. As for pricing, I don't know your area well but I pay my housekeeper appx $30/hr and she comes once a month and is here anywhere from 5-6 hours. I am charged more because of the house size. She and her hubby take their daughter to school then then have at least 1 house a day that they clean then pick up their daughter. I always pay cash.
Best wishes to you!!
PS.. as far as advertising.. many schools put ads in the student directories which are reasonably priced. Of course the best advertising is positive word of mouth!