[For some odd reason this question got moved to a different section of this forum. It seems to me it would have been better to leave it where it was in the Retirement section since it clearly relates to retirement savings and reporting of distributions from retirement accounts.]
Rollovers form a 401(k) are not subject to the one-rollover-per-12-months limitation. That limitation only applies to a rollover from an IRA (traditional or Roth) to the same type of IRA (traditional or Roth). A 401(k) is not an IRA. Whoever told you otherwise is misinformed.
Regarding your numbered questions:
1. Yes.
2. Not applicable.
To roll over the entire amount of each distribution you'll need to replace the amount withheld for taxes using other funds. Any excess withholding will become part of your 2023 tax refund. You might want to consider reducing tax withholding from other income sources if your 2023 tax refund would otherwise be excessively large.
