You may have several things going on to cause all the issue you are seeing. I'll do an easier one issue first, or at least to check that is.
The water heater
on electric, please provide a model number of the heater so we know exactly which vintage you have. The model tag is outside behind the drop down white door.
1. There is normally a dedicated 15 amp circuit breaker in the power converter for the water heater. Check if that is on. It will not heat without that on when plugged into shore power.
2. Your vintage heater may have a small on/off rocker flip switch on the back of the water heater itself. That switch is in a real hard place to get to many times, it has to be on to get the electric element to work.
3. Sometimes prior owners upgrade the water heater electric switch to have one of their own out in an easy location as it can be really hard to get to the little switch on the back of the heater. Not sure if yours was ever converted, but something to check, it would need to be on.
4. The actual electric element is burnt out. This is a common issue as if the water heater was empty, (no water inside it) and someone accidently flipped the switch on, it would burn out the element in short order. A few minutes or less. Once burnt out, the element has to be replaced and that can be a job all by itself pending where the heater is mounted. That element can be froze (corroded) in place and a real bugger to get out. If this happened to the prior owner, they may have just left it and only used the gas as it can be hard to change it. The element itself if not that costly, assuming you can get the old one out and not damage the tank threads. If the tank threads are damaged, then the whole heater can be bad.
Have a look for the first 3 items, they are the easy ones to correct. There is a way to test with a volt/ohm meter if the element is burnt out, this takes someone with electrical background to do on 120 volts AC.
The power converter,
again here is is good to post the brand and model you have. Pictures really help too. We and you have no idea if a prior owner changed out the original to some other brand. Sunline changed models/brands as the years went by so do not exactly know which you may have.
I'll give some big picture things that may help, the fans in the converter may be on a thermal sensor and will not turn on unless the converter gets hot enough to need the fan. Not all converters are like this, but many are. So the fans not working could be normal.
The clicking, again needing to know the brand and model. That clicking could be a problem that the converter is not working. And you said the lights inside do not work on battery alone, but do work when the converter is plugged in, yet you get clicking.
One other very important part, the battery voltage. We need to know the exact voltage number with at least one decimal point. When the converter is working and connected to the battery, the voltage should be at least 13.3 volts and could be 13.6 volts. If the voltage is truly 12.0, the battery is very discharged. 12.7 volts is 100% charged, 12.10 is 50% discharged and 11.51 volts is 10% charged or 90% discharged close to dead. As you can see, we need the exact number your meter reads.
By knowing the voltage, at the battery, we can tell if the converter is even working. If the converter is connected to the battery and working, the voltage will be 13. something
It may be your type of converter has a relay (a high power switch) inside it to control the charging to the battery and allow the battery to supply power to the camper. This is where the brand and model come in. The newer power converters do not have this older relay feature and are more automatic. Relays do go click and can chatter when they get told to turn on and something keeps turning them off.
Give us some more to go on, pics of the converter, make/model and the exact voltage at the battery and we can help more.
We have copies of the owners manuals here on our site, when you are logged into the site, you can download a copy for free from our files section.
In case you have not yet found our FILES section, there is a lot of great resource info in there. Including most all of the sale brochures from way back when, owners manuals, appliance manuals and other good stuff.
The sales brochure has a lot of good info on your model camper that is hard to come by in one organized spot. Just scroll to your year and download a copy. Same for the owners manuals.
To get to the FILES section, you have to be logged in. Look up top along the forum for the words "FILES". That is a tab, click it. Then select the area you want to go to can read on for hours, days, maybe even weeks...
A heads up, RV camper owners manuals are not like an automobile owners manual that gives exact instructions on most everything in your auto. The camper owners manual talks more in general and things to help you along the way. For the actual appliances, there are owners manuals with very details info on them from the manufacturer of the appliance. We have many of those in the files section too. If your model is not there, give us the make and model no. on the appliance and we can help search for it too, then add it to our files section for future help to others.
The water pressure,
We need some more info on this. Does the cold water have good pressure at all the faucets and the toilet? Are using using the onboard water pump with water in the fresh tank, or are you connected to city water?
We are here to help and we know you do not yet know all what to give us as this is all new to you. We understand, you work with us and we will try and help.
For the future, try and pick one area not working per post. It can be easier to get good info one at a time. The trouble shooting can get pretty deep sometimes and it is easier and more clear if one topic at a time is being discussed.
Hope this helps