Can you apply for a work permit in Thailand without a specific employer?

You can look for a job, if you find one then the employer will need to give you all the paper work to go with it. I'm not sure if you need to leave the country to apply for an business visa, I did something similar years ago (2004) I needed to go back to Oz for my business visa, with all the paperwork I was given I can't remember how long that took. Once I had that, I few back to Thailand and the companies agent helped me through all the paperwork to get the work permit, I remember there's lots of signing papers involved. May be different now.

Nope. To get a work permit you need a job. To get the Non B visa that allows you to get a work permit (assuming you’re not married to a Thai or have Thai kids) you need a job or offer of one.