Would "Act of God" defense apply if bricks fell off a building during a rain shower, if the building was in disrepair?

Potentially. Consult an attorney ASAP.

Do I have case for malpractice?

Consult a medical malpractice attorney to review the medical records and advise you as to whether the doctor breached the required standard of care.

More facts are needed to properly evaluate whether you have a claim and to answer your question.

Is the date Physicians Insurance receives my final settlement claim the date that is looked at for the statute of limitations?

No. Contact an attorney ASAP.

Can I sue a target store where I had a slip and fall they have me 30 days after that they offered me a 25 dollar gift card .

Consult a personal injury attorney ASAP to investigate the incident, save crucial evidence and protect your rights.

Tenant breaks lease after 5 mo of 12 mo lease, can I charge travel expenses and re listing fees?

No, but they do owe you seven months rent. You're likely not to recover this so I would just cut your losses and rent property to another. Best of...

Can I sue for refusing to refill necessary medications

Sorry for your experience but you just need to switch doctors.

My daughter was in a severe car accident and the money from the settlement was put in a trust funds for any needs she may need

That percentage sounds high and you are permitted to switch to a lower percentage trustee.

I was called a sex offender repeatedly by a security guard in front of 12-18 kids, and 6-8 adults. Can I sue for slander per se?

Consult a local attorney because it appears that you may have a valid claim.

Can I press charges and/or file suit against online harassment and libel?

I agree with Mr. Lassen's approach and advice.