Hello and thank you for contacting us. This is Dwayne B. and I’m an expert here and looking forward to assisting you today. If at any point any of my answers aren’t clear please don’t hesitate to ask for clarification. Also, I can only answer the questions you specifically ask and based on the facts that you give so please be sure that you ask the questions you want to ask and provide all necessary facts.
Unfortunately. OH is what is known as an employment at will state. That means that, basically, an employer has the right to do almost anything so long as it doesn't violate the laws against discrimination or harassment due to race, age, gender, etc.
As to your specific questions:
1) Yes. There is no law that would prevent an employer from giving two write ups in this situation.
2) They can take any sanctions they want up to and including terminating his employment for insubordination.
3) That depends entirely on the company policy and what has been done in the past there at the company. The law doesn't mandate how vacation time and PTO works.
4) They are incorrect in that they are allowed to accept a doctor's note. They are operating under a misunderstanding of the Americans with Disabilities Act. However, what they are doing is not illegal, they just don't understand the law.
If your friend is operating under a written contract of employment then the terms set forth in that agreement are what applies. Since most people don't have a written agreement, the answer I set forth above apply in 99% of the cases.
There is a document at the following website which explains employment at will in Ohio. I always provide a link when explaining how this works because most people are under the impression employees have more rights than they actually do. That link is: http://www.lsc.ohio.gov/membersonly/126employatwill.pdf