You CAN access the rolled over amount immediately, but you will also have penalties if the amount you are withdrawing hasn't been held for the required amount of time to be a qualified distribution. If you convert part of your 401(k) to a ROTH IRA, you're still under the 5 year rule since the funds are "new".
As far as the earnings go, when you withdraw funds you can't "choose" which part of the funds you are withdrawing (contribution v. earnings). The converted amount will contain both contribution and earnings.
The amount you are converting will produce a taxable event in the year you are converting to a ROTH because your 401(k) funds were pre-tax. So you'll have to pay tax on the amount you are converting.
If you take a distribution from the ROTH before the end of the 5 year period, it's called a nonqualified distribution. You have to include the earnings part of your conversion in your gross income, but the basis is not included.
Following is the IRS guidance on this subject.
IRS Retirement Plan FAQs on Designated ROTH Accounts
IRS Rollovers of retirement plan and IRA distributions
The thing to remember is, it's your money, if you need it, it's there for you. You will pay a bit more, tax-wise, but if you need it, you can use it.
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