You can call 1-800-829-1040 do not select Option 1 (refund).  Select the option for personal tax return and follow the prompts for a live representative. The person that you speak with will have direct access to your tax return and be able to provide you with a status update.

I need the date that TurboTax accepted my e-file of 2018 return and date it was accepted by IRS

You would have to call and talk to an agent to get that information, as mentioned by CarissaM.