You really have to remove the tank to scrub the sludge off the insides unless there is a large inspection hatch on the tank top. Emptying it will not eliminate future problems.

It makes sense to use a small solar panel to keep the batteries topped up if not on shorepower for charging. The bilge pump should be wired to the batteries in the normal manner.

You shouldn't have to remove the caps to install the antenna. After drilling a hole for the wire either in the top cap or the mast side below the cap (I have seen both methods)  use a messenger line with a nut that fits the hole tied to it and feed it through the hole. If not tie a small line to something already in the mast, a halyard or wire and use it to pull the messenger up. Add the wire to this and pull both back down. The last time I did this the boat was afloat with the mast up and it went well working from a bosuns chair.