1) Standard silica is considered mildly acidic, while aluminum oxide is considered basic (more basic than silica is acidic, if you ask me). I've never used aluminum oxide, but some of my colleagues did to isolate things like amines (which drag like a mofo on silica). I spiked my solvent with a little triethylamine and ran amines on standard silica, so there are ways around everything. I'm not aware of other media, unless we start talking about things like size exclusion or ion exchange chromatography.
2) You can use a low grade silica for a flash column, though if you have close running spots a higher grade can really help the separation. If this is something you're doing purely for self interest, get a lower grade. Higher grades cost more, and the prices increase very quickly. We use 60-200 um particle size and it's a good general starting point. This is the brand we currently use:
http://www.silicycle.com/products/siliaflash-irregular-silica-gels/r10040b3) I've never dried silica, even in very humid climates, and it's always worked fine.