Changes moving to long-term disability

I am 60, and this year underwent a significant cancer diagnosis and treatment. This month I moved from short-term to long-term disability, and was just approved for Social Security Disability, which will partially offset some of my LTD insurance pay (which is 50% of my base salary). I also will get to remain on the company's medical plan.

 

My questions involve what tax changes I can expect in this new status, besides a general lowering of taxable income due to a 50% salary reduction. My first LTD payment from the insurance carrier last week deducted for my medical premiums, as well as estimated federal and state withholding. However, they are not deducting for the Medicare employee portion. Is that paused while on LTD? I met my OASDI withholding limit earlier this year so I also want to know if that is paused while on SSDI. 

 

I expect it's likely I may remain on insurer-paid LTD, with a portion offset by SSDI through either 65 or my full retirement age of 67, so I don't want to make a mistake on tax planning. Thanks!