How can I apply for an E-2 visa while in the U.S. on a B2 tourist visa?

This is an involved situation. You need a consultation appointment with an immigration attorney.

It is doable. You could contact an experienced immigration lawyer to help you through the process.

Yes, definitely doable.

You need to buy a business or establish a new business based on a substantial investment in a business that is real and operating. It is difficult to advise you to hire counsel but you need to have a qualified professional who can guide you through the process. Also check USCIS website as they have a lot of information. We advise you to have a business plan and a real business with at least $150,000 invested but that varies based on the type of business you are planning to run.

It is doable but keep in mind that after your status is changed and you then depart the U.S., you will need to be issued an E-2 visa at a U.S. Consulate, which may take some time. This should be orchestrated with experienced counsel.

Yes - you can change status in the U.S. from B-2 to E-2 with USCIS. This can be done using premium processing and you will receive a response in 15 days from USCIS. If you want to travel abroad in the future, you will have to obtain an E-2 visa appointment at an embassy/consulate in your home country before you return to the U.S.

After the 90-day window, you no longer have an issue with immigrant intent. Bigger issue is whether you have an investment identified and can work fast enough to file the change of status in the 3 remaining months. Given the time frame, a packaged investment offering would make the most sense.

File an application for change of status and provide proof of your eligibility. Hire a lawyer if you need help.