Do not take what I am about to say as a negative , or any reason to not learn
There are a lot of issues here , 1st up the almost total lack of knowledge about too many things .
Not having a multi-meter , and not knowing how to use - I do not have a good memory but will try to get the point across ,
Lord Kelvin " I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind. "
Lord Kelvin
Do not make assumptions without a knowledge base - as an example thinking there is more voltage with fridge plugged in .
To start , I would suggest spending as little as possible with projects that do not matter , as an example some LED lighting that is only connected to a small solar panel , maybe 5-15 watt [ problem here is there are premium pricing on small panels ] typically $2-3 per watt & up , while panels that do real work can be as low as $1 per watt , I would suggest never to send more that $1.50 per watt [ except for flex-able / folding , small ] - generally they command higher pricing .
So after getting that small panel , LED light , next start with a used car battery , free - if not just the core charge for not having one to trade in when buying a new battery .
Next is metering [ not a multi-meter ] but meters that are always connected - so at a glance you can see whats going on - to do this get a panel volt meter and a panel amp / current meter , these can be found as cheap as a couple bucks each , but they do need to be rated for what ever numbers are expected to be , in the above case 25 volts [ a 12v solar panel open voltage can be as high as 22 volts ] with nominal around 14v .
Then a amp / current meter at maybe max 3 amps , you want low amp reading because the system above is going to be averaging less than an amp for charging / draw .
All of the above should be less than $75 , now after getting use to the values of solar / battery / charging etc. , you get a grasp of these numbers , and how each device works , you can buy / build without ripping yourself off , like spending twice as much as need on the wrong battery , solar panel - 3 to 6 times as much .
With low power use & charge with above - no need for charge controller .
When charging from engine running , remember that there is vary little , if any charging at idle , average charge rate of alternators these days is 90 - 160 amps , and that only happens as higher engine RPM's , like min. of 1,300 RPM + .
Some of the biggest issues with mobile solar are not enough area to supply enough energy , or enough area for enough batteries for what most want or think .
Take over the world - put panels everywhere