I take levothyroxine for underactive thyroid. Will this show up on a pre employment drug test for walmart?

No. Levothyroxine is bioidentical to your own thyroid hormone. No abnormality will be present as long as you are taking the proper dose.
Depends. Not sure what they are testing for. There are drug screens that will identify the presence of any medication/drug, but most likely they are only testing for illegal and/or addictive drugs such as amphetamines, cocaine, opiates, and possibly benzodiazepines.