Yes, you should complete your profile with the make, model, engine, etc of your MH as they're all different, but maybe this will help.
You'll probably have two places to use the hose. One will be a screw on hose connector that will have a valve which will divert the water into either the MH water system while not putting any water into the tank, or the valve will divert it into the tank. The other place you can put the hose is a place where you just stick the hose into a hole behind a little flapper door that usuaully has a lock on it. The hole will just fill your water tank.
Go inside the MH, make sure the water pump is turned off and open a faucet to remove any water pressure in the system. Then with the hose hooked up to the threaded connection, go inside, make sure the water pump is turned off, and open a sink faucet to see if you have good water pressure. If you do, you're using city water and not filling the tank.
If you have no water pressure, then the hose is probably filling the water tank. Watch your fresh water tank gauge. While MH gauges are not accurate, after 10 - 15 minutes, if the water is going into the tank the gauge will show some an increase. If you're in a quiet area you should also hear water going into the tank. You can turn on the water pump and you should get water after the pump builds up pressure. You may get a lot of air or bubbles until they get out of the system.
As for your fresh water drain, the mfgs hide then in all sorts of places. You should sanitize your fresh water tank once a year. Put either sanitize or bleach in the search block for directions. Don't worry about traveling with the tank full of water. The DP won't notice the weight and you never know when you'll need the water while traveling - think of flushing the toilet......
Bill