What would happen if you mixed equal amounts (example: 1 mole each) of
all the non-radioactive elements (1-83 except technecium)? i.e. what
compounds would form?

What's wrong with technetium?

The most electronegative elements (fluorine, chlorine, oxygen, etc)
would react with the most electropositive elements (cesium, sodium
calcium etc) to form salts.  Other than that, I don't think much of
interest would happen.

Even if you mixed all the elements together at an elevated
temperature, most of the elements are metals, so you'd end up with a
big mass of metal alloy, with a "slag" of oxides, halides and maybe
silicates floating on top.

Well the first things to bond (because of electronegativity) would be
the most reactive Metals and non metals Like fluorine for instance. If
your looking for the real mechanics of electronegativity look for the
shielding effect of ions. If for some reason water formed, you would
get several oxides from the Alkali metals. There is also the
probablility of strong acids forming and Acid Base reactions but I
wouldnt hold my breath.