A good agent has contacts and can get your music in front of decision makers.
Agent can refer to a manager but is generally referred to as a booking agent in the music world. There are talent agents, casting agents, etc... But that is for the acting world.
Co-writing is hugely valuable, both as a skill-building tool (there is always something to learn from another write!), an opportunity to have another writers team push a song you have co-written, as well as a way to network. It usually is a building process. You start writing with up and coming writers and work towards writing with hit-writers.
The best thing is to keep playing your music and honing your skills. Generally, you don't need a manager until there is something to manage. Keep in mind agents and managers make a percentage of the money you generate. If you are not producing sufficient income, you can always hire services from a company that can help develop you as an artist and get you to the next step in your career.
The most important people in the career of an artist is a mentor. Don't be afraid to ask people if they can be a mentor. The worst that can happen is they say no.