You're welcome.

* I'm not renowned enough for the self-name approach (and there is an unrelated collision with a known figure in the field). I had also gotten advice that single person shop names were a filter for some potential employers. I'm not trying to misrepresent myself, but want to make it past a filter

For me I wasn't trying to sell myself to people who didn't already know of me. Different situation. Oddly enough, there is another LLC with the same name as mine one state over, in a different business. We are friends on LinkedIn in, just out of curiosity.

* Something like fidelity.com - Self employed ?

Exactly the one I use. The max contribution this year with catch up is $83,250. Helps to knock down the MAGI to try to qualify for ACA tax subsidies.
Also do HSA contributions and spousal traditional IRA. Every little helps.

I usually bill by the half-hour. Sometimes take on a fixed-price job if the scope is well enough defined. That's rare in my business.
Billing rate? It's tempting to go low to get business. It takes many years to recover from that.
2-3x what you'd get as an employee. I'm about 2.5x