I run all my short-wave and scanners of 12v car batteries:
[...] I use wet batteries with caps so I can add water as needed

Good idea!

The batteries I used were all former car ones. A semidead car battery
can still work fine for a couple of years on light duty like receiving
or QPR.

Having caps is useful for another reason: when I got a
new-old-car-battery I flushed all the acid out from a cell at a time,
and cleaned the fluid by letting any muck settle on the bottom of a
thoroughly cleaned and distilled-water rinsed plastic basin. I then
transfered the liquid into another clean basin, used it to shake-flush
the cells, and drained them into the 1st basin again. Repeat a couple
of time, then refill the cells, then add distilled water as needed.

Advantage: evens out the deviant cell (there's always one worse of
than the rest), reduces risk of shorts.

Risk: THERE WILL BE ACID SPRAY AND SPLATTER. Better work with a thick
apron, gloves, and goggles. A drop on your skin won't hurt you much if
you clean it up and flush immediately. A drop on your clothes will
drill a hole in them unless you wash them right away. A drop in your
eye is going to hurt you permanently.


and have a plastic box for the
house battery.

Hmmm... I kept my house battery OUTSIDE, on a small balcony. When I
was in the army, we had a truck battery recharging room that was force
ventilated, and we were forbidden from spending any idle time in it.
We were told that there was an explosion risk (oxigen and hydrogen
from an overcharged cell) but I did not like this idea of loitering in
the company of sulphuric acid and lead for any length of time. OTOH,
if your plastic box is almost airtight, just run a tiny ventpipe (eg,
a fuel line) to the exterior of the house. Keeping the battery warm
improves its performance. One thing seems clear: explosion danger is
minimal, and neither lead nor sulphur are an issue if in trace
amounts.


Grounding antennas and mast:
I use a telephone grounding block on the antenna leads at the first
place it touches the house grounded to a ground rod, all of this is at
the bass of the mast. I put the bottom of the mast about 6 inches in the
ground beside the ground rod. Because I live in the dessert I have 24
rose bushes on a drip watering system so I just added a drip at the
ground rod and it and the mast get 20 minutes of drips twice a day. I
also ground the sheath on the coax cable I use to feed into the house
and garage and keep ALL THE ABOVE AWAY FROM ANY AC WIRES OR LIGHTS.

Well done! The grounding point is also the best place to put a
lightning "arrestor". Better run more coax to a directly grounded
arrestor than any wire between the arrestor and the grounding point.

Many years ago, there was a 1-bolt storm about 8 miles from my place.
I heard the arcing from an abandoned, ungrounded 50 ft wire antenna
across a banana socket and into a grounded metal panel. Overt 30 sec.
later, I heard the bang. The bolt caused a lot of damage in the nearby
city, but would have killed any unprotected front end at my location
as well.

Another trick I use is that of the "ground reference". I strap
together any and all metal objects inside the shack with as broad and
short pieces of copper sheet as possible. This is normally done in
professional installations. The reasoning is that strapping all the
equipment cases, cabinets, racks, pipes, tables, etc. builds a common
capacitive sink that parallels the effect of grounding at RF. As you
say, a nearby bolt can fry radios at a distance. That's RF. If you can
dump some of that energy, even inside the house, better for your
equipment.