Who should be paying for my Dad's ongoing/recurring medical bills now?

A good lawyer can find your dad doctors. Get one quickly.

What is my recourse

Yes. Your best bet is to just find a new lawyer you trust and let them take over from there. They will get the file from your current firm. The...

Can I do Medical malpractice?

Unclear. You may have waited too long to sue.

Are punitive damages included in total amount of claim?

Wow. These nuts and bolts questions are impossible to answers on a site like this. You need a lawyer.

You need a lawyer. This kind of nuts and bolts stuff is impossible to answer on a site like this.

This company doesn't seem to be taking this matter seriously. Which kind of legal representation should I seek?

You might do well with what's called a lemon lawyer. Look into that.

Do I have a case?

You've figured out that this drug was affecting you years ago, so regardless of any liability on whoever makes it or prescribed it to you, it's...

There is more to the described situation but truly the contingency fee is the necessary ingredient to any pursuit.

I read this whole paragraph and I still have no idea what happened. What happened? Put it plainly.

Medical Resident told to prescribe the wrong drug for a condition by the Doctor training her.

if they were both at fault (like an attending and a resident), you'd sue them both as well as their facility. Get a lawyer for this, you can't do...

Statute of limitations on auto accident case killing pedestrian. Claim of minor children of the deceased.

That's generally correct, unless a government entity is involved. You should act fast to get them a lawyer and get the case started.