In reply to Suncream:
From experience I have found ice pillars to vary depending on what forms them. A frozen stream running over a cliff will likely form a more hollow cylinder than a pillar formed from seepage, runoff or melt. Of course this may not be obvious from below.
Ice formed from slow seepage over time will initially form a dagger and an amalgamation of organpipes which in theory would be more stable and thus easier to protect, but may not get very big. Both streams and seepage pillars build as ice stalactites and stalagmites until they meet in the middle to form a pillar. Streams will normally have a big cone of cauliflower ice at the bottom. Streams are also more likely to have wild ice structures such as jellyfish as well as wind formed features such as cobras and big umbrellas.
Its not uncommon to reach the top of a pillar on a stream and find a glass like window of ice with water running behind giving you a view into the deep black abyss you have unknowingly climbed the front of.
With assessing such features I normally look for nice blue ice, anything white or grey is likely thin, aerated and possibly sun baked. Fresh chandeliers and small amounts of water will help indicate if the ice is still growing. Smooth rounded surfaces and smooth depressions will indicate sublimation of the ice. Hollow sounds are unnerving and will indicate thin ice. Of course recent weather and temperatures are key to understanding stability of pillars and petzl has a nice simple overview on this: https://www.petzl.com/US/en/Sport/Waterfall-ice-study?ActivityName=Ice-clim...
With protecting something like this, a solid screw in thick and consolidated ice at the base is best starting point (Although often most people will build a belay behind big pillars, in the EU there may even be bolts). Otherwise, you can often find very solid ice in a flat platform behind the pillar, which can take a long screw and an extender. If the pillar is short and you are confident you can gun the face and protect the top out by placing a screw in the ice above where the pillar meets the rock. The more solid the pillar sounds (subjective), the better its likelihood to take screws. Screamers can add piece of mind for screws in the pillar itself.
Personally hollow sounding pillars terrify me, tho this may derive from some Senja induced ptsd when one discovers the pillar isnt actually a pillar and rather the stumpy remains of one.