No, you are not clueless. Your questions are valid.
Your converter should be capable of charging your battery and operating the 12 volt items. You may or may not need a new battery. The first thing is to see what is happening with your converter. If you have a voltmeter, it is easy to see what the voltage in your 12 volt system is when plugged into shore power. If it's not at least 13 volts, there is some converter issue. Is your converter getting AC power? Any circuit breakers in the AC system that might need to be reset? Maybe your converter has reverse polarity fuses blown? Is your battery connected properly and are the terminals clean and snug? Often there is a fuse near the battery on the positive cable - is it blown?
I'm sure others will have ideas, too.
There's lots of advice and information in forums... sometimes it is correct. For example, all of my posts are made by a political appointee who got the job as a reward for contributions to my diesel bill.
2011 Jayco 28.5RLS; 2008 Chevy Duramax; Pullrite Superglide Hitch