Does a base have a pH greater than 7 and has more OH ions than H ions in solution?

Answer 1

The answer is a little more complicated than just "yes" or "no."

Something which, in water solution at 298 K, has a pH greater than 7 and more hydroxyl than hydronium ions (which is basically a slightly different way of saying the same thing) is indeed a base. That's not precisely what you said, and the differences might be important, but it's pretty close.

However:

The dissociation constant for water is different at different temperatures, so what constitutes "neutral" is actually temperature dependent (that's one of those subtle differences I said might be important).

A pure base, one that isn't dissolved in water, may not technically have a pH because there are no hydroxyl ions, and the log of zero is undefined (there's another).

Finally, there are bases that have nothing to do with water and hydrogen/hydroxyl ions (this is probably the most significant thing keeping the original statement from being "close enough" to just say "yes" to). Look up the term "Lewis base" if you want to know more about these.