It sounds like you've had a rougher than usual introduction. It should get better. Through your own trial and error, and preferably, knowledge from this forum, you'll figure out solutions to all the issues and become a successful, seasoned commuter.
My first recommendation would be to learn how to do as much of your own maintenance as possible. This will save untold amounts of time and money. Once your bike is in good working condition, you'd be surprised how little maintenance it takes to keep it that way. Main tasks are cleaning & lubing chain; & fixing/replacing flats. Riding in wet conditions will drive chain/drivetrain maintenance requirments up considerably. Fenders will offset that to a large degree.
If it is a crapmart bike, I'd recommend that you start researching what better quality bike would meet your long-term needs. If you're serious about commuting daily, you'll be much happier with a good quality bike that doesn't introduce avoidable issues into your commuting regimen.