How do you safely clean silver plate candelabra?

Use a soft cloth and a mild silver polish. Abrasive cleaners strip the thin layer of silver right off the copper core. Never dip them in liquid chemical baths. The fluids get trapped in the hollow sections and corrode the metal from the inside out.

My grandmothers candelabra has got this green buildup inside the little cups where the candles go, what is it and should I scrub it out?

That green residue is verdigris. It forms when the copper in the base alloy reacts with moisture or acids in old wax. You can soften it with warm soapy water and a wooden toothpick. Avoid using a stiff brush because it scores the metal underneath. Once clean, a small dab of microcrystalline wax stops the damp getting back to the surface.

Can you wire old candelabra for electricity?

Many dealers do wire them. The hollow stems make it quite straightforward to run a modern lighting cable up from the base. You usually have to drill a small exit hole near the bottom edge. Some purists dislike this alteration, but it gives an unused piece a practical function on a sideboard. Make sure an electrician does the actual wiring. Old metal conducts electricity, so the earthing has to be spot on.

I want to use my brass candelabra on a dining table but they wobble a bit when touched, is there a way to fix the bases?

A wobble often means the internal resin weighting has dried out and shifted. Sometimes the baize pad on the bottom has just worn unevenly. Turn them over and look at the baseplate. If there is a central nut, tightening it gently might pull the whole structure back into line. If the base is warped, a restorer can gently tap it flat using a hide mallet and a sandbag.