You may go to the web site of Patent and Trade Mark (http://portal.uspto.gov/external/portal/pair)to look for the answer by yourself or call a patent attorney that might be an easy way to get what you want to know.
For the second question, you'd better to review the contract you sign with your company. There might be clear deion to identify if your idea is work related or not. If I were you, I would like to contact an attorney to see what is the answer from him/her.