Well I will try my best to answer your questions from a client viewpoint
1. There are thousands of scripts that can automatically create new email accounts, try searching hotscripts.com for free ones.
2. There is no real way to stop spammers, if they are intent on doing something then they will. However, you can record their IP addresses and/or limit the number of emails they can send each minute.
3. I would not recommend a small fee, unless you think your email service is exceptional or if it would be your only source of income. Personally I wouldn't pay any money when I can use Gmail (which I find to be extremely good) for free. You must have something special which will make people actually pay to use your email service, if not they will choose the larger companies like Gmail, Hotmail, or Yahoo. If you do not have a fee, then you will definately have a lot more users.
4. I'm sure there is a way to configure the email script so that you can send google advertisements with each outbound email. Also, putting an advertisement on the mainpage wouldn't hurt either as long as it does not disrupt the look of the site. Again, I can see your reasons for doing this (from a financial standpoint) but I can assure you that almost no companies do this. If you do this, you are compromising your customers because the majority will switch to a free email provider unless you truly have something unique which the other email providers do not have.
I would NOT pursue this idea because, no matter how hard you try, Fartmail.us isn't the most appropriate name for people of all ages. Also, gmail and hotmail have thousands of employees working hard to improve their email systems... it would be almost impossible for one person to compete with an entire corporation. For a name like Fartmail.us, I would probably turn it into a joke/forward/comedy website that lets you send the joke to anybody. You can then attach a google/yahoo advertisement on this email and hopefully make some money (trust me though, few people will click).
I'm not too much of a domain expert, but I think you should forget about making anything out of fartmail.us. The domain doesn't seem to be worth much and there really isn't too much you can make out of it. The best you can hope for is someone will offer you something in the $xxx range for this domain.