First step is to take a deep breath. You appear to have several things going on and lumping them all together will make them impossible to correct.
1st. Brakes. In normal operation the brakes have nothing to do with the 12V [power system in the trailer. only if the breakaway switch is activated does the trailer 12V supply become involved. Using the meter, check the voltage on the brake pin of the TV connector when the brakes are activated. If no power there issue is in the TV ( possibly a fuse). Many Tv's have a separate fuse for the trailer brakes and for the trailer lights. If you have power at the connector, then check for voltage at the brakes ( usually wire nut connections near the wheels. If you have power there, you should be able to hear the brakes activate ( click) when peddle pressed. To confirm, jack trailer ( by frame not axle) spin the wheels and tap brakes. Wheel should stop.
Once you get brakes fixed, you can move on to trailer battery. The fridge and aux stuff will drain the trailer battery. You can get some help from the 12V aux circuit in the trailer plug if connected properly. Many vehicles have this circuit wired up but do not put a fuse/breaker in the panel to save money. If you do not have 12V on the aux pin check the owners manual for the fuse position and look for a fuse. Also check the TV fuses for the trailer lights. They are usually separate from TV lights and in a separate panel.
If the 40A fuses in the convertor panel are blown, you will not charge battery when plugged in. These fuses are usually orange. If you can get to the battery, check voltage with TT disconnected from shore power. A good battery will be in mid 12V range. Then connect shore power and recheck voltage. If working properly, voltage should now be in high 13 range.
Remember anything working on AC in the TT ( AC, Microwave etc) goes through circuit breakers, Anything working on 12V ( fridge control, lights, water pump, furnace) works thru fuses.
If you break this effort up it should be a relatively easy problem to fix.
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