Contra dancing is an informal activity. There is no most-appropriate dress -- just wear confortable, loose-fitting clothes. The dancing is lively so be prepared to stay cool.
Wear soft-soled or leather-soled shoes. We dance on wooden floors, so be sure the soles of your shoes are clean and without nails, etc. Don't wear shoes that stop you from sliding and pivoting.
No. Appropriate protocol is to take a new partner for each dance. So come alone, or bring a date, your spouse, or a friend and be ready to have FUN!