Yes. Credit unions can offer credit cards along with most or all of the services people typically associate with banks, such as checking accounts, loans, investment services, and business checking.
If you belong to a credit union, the staff will typically try to work with you to help you get access to the financial services you need as a member. So, for example, if there's a problem with credit scores, it may be easier to get the credit card you want from a credit union, compared to getting a comparable card from a bank or other financial institution.
A credit card from a credit union works the same way as a credit card from a bank or financial institution. However, because credit unions are member-owned, they may charge lower rates and offer better rewards to satisfy member needs.
Yes. There is typically a balance transfer fee when a sum is transferred to a card.