Solo 401K for additional 1099 income

Wow. There is so much here. Each of your questions is essentially a separate discussion thread. However, in brief:

• For an individual 401(k), you simply contact one of the major brokerages, do the paperwork, and that's it. I previously had one at Vanguard, but I moved it to Schwab last year after Vanguard sold off their small business retirement accounts business to another firm. I've been happy with Schwab's Individual 401(k) so far.
• Given that you still have W-2 income, consider a SEP IRA instead of an Individual 401(k). In your particular situation (maxing a reguler employer-sponsored 401(k) and wanting an additional account for self-employed contributions), they would function identically; the only difference is that the Individual 401(k) has the ability to make employee contributions as well (which you are already doing through your W-2 employer). (Note that a SEP IRA is counted the same as a traditional IRA for the purposes of the back door Roth IRA contribution, so if you make use of the back door Roth IRA and intend to continue doing that, then you need to stick to the Individual 401(k) to avoid problems.)
• As far as quarterly taxes, there is not even a way to guess at that. Fundamentally, you need to project your self-employed income, estimate your total tax burden (self-employed, W-2, interest, capital gains, etc., for both you and your spouse), then divide the shortfall by 4 and make the quarerly payments.