Critter-3's information regarding the 401(k) contribution limits is somewhat incorrect. The $57,000 limit for 2020 is a per plan limit, not a per individual limit. It's the $19,500 per-individual limit that applies just to employee elective deferrals and Roth contributions to all plans in which the individual participates (except for 457(b) plans which have a separate $19,500 limit).
I'm going to directly address the original questions, so some of this might repeat what has already been said:
The sum of your employee elective deferrals and Roth contributions to the solo 401(k) (traditional or Roth) and the 401(k) at your W-2 employer is $19,500. This limit is per-individual. Assuming that you contribute nothing to a plan at your W-2 employer, you can split a total of $19,500 employee elective deferral and employer contributions any way you like between the traditional and Roth accounts in the solo 401(k).
The $57,000 limit is a per-plan limit for employee and employer contributions combined, however your self-employment income of $100,000 is far from the amount that would support that much of a contribution unless your solo 401(k) plan permits after-tax contributions that would take you beyond the $19,500 of elective deferrals and Roth contributions. Assuming exactly $100,000 of net profit from self-employment, your maximum employer contribution to the solo 401(k) would be $18,587 (all to the traditional account). If the plan permits after-tax contributions (and it might since you mentioned a MEGA backdoor Roth which involves after-tax contributions to a 401(k)), you could contribute the remainder of the $57,000 limit, $18,913 as an after-tax contribution to the traditional account in the solo 401(k).
You have enough compensation to also contribute the maximum $6,000 to a traditional IRA, but with your participation in the solo 401(k) that traditional IRA contribution would be nondeductible because your AGI will be above the limit for deductibility of the traditional IRA contribution. Your AGI will be too high to be able to contribute to a Roth IRA.
If your solo 401(k) plan does not permit after-tax contributions, the maximum that you will be able to contribute is $38,087 to the solo 401(k) ($19,500 employee and $18,587 employer) and $6,000 nondeductible to a traditional IRA for a total of $44,087. If your 401(k) plan does permit after tax contributions, add to that the $18,913 that I mentioned earlier. Depending on the plan rules, you might be able to make a rollover from the after-tax sub-account to a Roth IRA, but you likely will have to leave the other amounts and any earnings on those other amounts in the solo 401(k) until you reach age 59½.
Deferring income and getting money into Roth accounts are mutually exclusive. Even if you could make a distribution of the employer contributions before age 59½, whatever deduction you got for those contributions would be offset by the taxable amount of the rollover to a Roth IRA (or an In-Plan Roth Rollover, if the solo 401(k) plan permits).
You need to read the solo 401(k) plan agreement to find out what is and is not permitted by the plan.
