We have tried running a pump from the van's battery in 2 different vans and it didn't work for us.
However, there was another member on here with the same van as my son has and it worked for him.
It will be mileage related. We don't do much mileage so the battery never got a chance to recover its charge. The jobs the vans were on were very compact work so they didn't move much during the day. His van battery lasted my son 4 days before he had to 'bump' start the van to get home. We later replaced his van battery and we tried again but again his battery was flat in 4 days and we needed to get the jumper cables out that time.
I have watched a cleaner near me use both a leisure battery and a starter (car) battery, swapping them each day whilst the other is on charge.
The car battery lasted him 3 years and the leisure battery 3 1/2 years. At the tail end of the day he recons he broke even cost wise as the leisure battery was slightly more expensive than the starter battery.
A starter battery and a leisure battery are designed differently as they are required to do different things.
A starter battery needs to deliver a vast amperage of current to start the engine for a brief few moments. It then has nothing to do as the vehicles alternator takes over and supplies the current for everything with enough left over to top up the battery.
A leisure battery on the other hand will deliver a steady amount of current over a protracted period of time. Some leisure batteries do have a CCA (cold cranking amps) value on their spec sheet. These batteries will provide an occasional high power output (motor movers attached to caravans), but will be at the expense of durability. Their CCA is also lower than a starter battery.
Traction batteries however can be used in both applications, although probably impracticable in a van. They are usually 6v batteries cabled together to form 12v. They are also very expensive.
We are fortunate in being able to park the vans on the driveway. I nowadays just plug my charger in to recharge our leisure battery. The local windie who uses both batteries has to physically remove his every night as his van is parked in the street.
Webasto make vehicle preheaters which are found on numerous vehicles in the colder northern European countries. They can be programmed to automatically switch on and in about 30 minutes will warm the vehicles motor and interior and melt the ice on the vehicle's windows. To start a diesel Webasto requires short bursts of 15 - 20 amps for a couple of minutes, and once started will draw about 2.5 amps. So theoretically a preheater shouldn't draw that much current from the battery during that 30 minutes (5 amps at the most.) But they warn that a user must drive a journey that is as long as the heater has been on for to keep the starter battery charged up.
Our Shurflo pumps draw around 4 amps each hour, so if we apply Webasto's instructions to the letter, we would be driving a lot each day. I appreciate Webasto advice is erring on the side of caution.
You say you are a 'bit lost' by the wiring going to the fuse box - so this is what I would suggest;
Fit a leisure battery and if you so desire a split charge relay directly from your van's battery. I would then remove the wiring from the fuse box as I've seen some pretty bad automotive DIY electrical jobs over the years. Who knows what the previous owner has tapped into.