"Is it as simple as moving the Rollover IRA to new Company 401(k) then do the backdoor Roth IRA conversion immediately?"
Yes.
"What happens after I do the backdoor Roth IRA conversion, then decide to move my money back to a Rollover IRA?"
If moved back in the same year that you do the Roth conversion, it will be as if you never moved the funds to the 401(k).
"Is this okay, since when I did the Roth IRA conversion, I didn't have any other IRA or IRS will look and count for the whole calendar year?"
No. The timing of the Roth conversion during the year is irrelevant. The calculation of the taxable amount is done as if the Roth conversion occurred on December 31.
