2. Actually, $18,587 is a bit off. I didn't take into account that your net earnings from self-employment plus your W-2 income would exceed the $137,700 Social Security wage base for 2020. With $100,000 of self-employment net profit and $60,000 of W-2 income, the deductible portion of self-employment taxes would be $6,157. That means that your maximum employer contribution would be 20% * ($100,000 - $6,157) = $18,769. See Chapter 5 of IRS Pub 560 for the more complete calculation that includes factors that would only affect individuals with lower net profit. This would make the maximum after-tax contribution be $57,000 - $19,500 - $18,769 = $18,731.
3. The Roth 401(k) must be a separate account within the same plan as the traditional 401(k) account. You can't have a 401(k) plan without a traditional account and your can't have a separate plan for the Roth 401(k) account.
4. Earnings grow tax-free only in Roth accounts. Any earnings on funds in the traditional accounts are tax-deferred, not tax-free. There are no restrictions on your ability to do a Roth conversion from a traditional IRA. There are certain restrictions on your ability to do rollovers from the 401(k) to a Roth IRA, but if your 401(k) plan permits In-plan Roth Rollovers, there are no statutory restrictions on your ability to do an In-plan Roth Rollover (although there might be plan restrictions such as the frequency of such rollovers).
I'm not sure what you mean by a Roth-IRA conversion ladder. Partial conversions are permitted, so you can convert as much or as little as you want in any given year, allowing you to manage your marginal tax rate. However, if you make a nondeductible traditional IRA contribution and you have no other funds in traditional IRAs, you would generally want to convert the entire traditional IRA balance immediately since the conversion would be essentially nontaxable (except for possibly a small amount of taxable earnings while in the traditional IRA if the conversion does't happen immediately).
