Itr for ay 2018-2019 not processed

Let CPC take its own time to process earlier ITR . So many ITRs are being processed in this month, yours may also get its turn. 

Yes, you can file your ITR for AY 2019-20 without any problem. But wait till next month for final TDS credits.

Yes, you can file your ITR for A.Y 2019-20 irrespective of processing of ITR for previous year.

Refund, if any is due, is issued only after processing is complete. Normally after verification, the 'status' of your tax return would be 'Successfully Verified' or 'Successfully e-Verified'. After processing is complete, the status would be 'ITR Processed

They have started processing returns of AY 18-19. Recently lot of intimations are being sent.

Wait for a week or two, yours might get processed soon.