A. Yes. Many people have both a short term disability policy and a long-term disability policy to cover different types of scenarios (e.g. if you become permanently disabled vs. being temporarily disabled).
Many people who have a group DI policy through an employer supplement it with an individual DI policy if they feel the group DI doesn't provide enough benefits or a very good "definition of disability" - when buying disability insurance, make sure to understand the definition of disability that's being cited in the program (own occupation, modified, or gainful - this is the most important factor in your disability policy as it will determine if you are eligible for a claim when something happens).
Note, disability insurance policies coordinate benefits so there's a limit to how much coverage and what kind you can secure (most carriers will keep it to a maximum of 70% of income - the percentage can vary by insurance company).