I pronounce it ah-LEE-sha and I'm in Australia. This is how nearly every
Alicia I have known has pronounced it although I have known a couple who use the three syllable pronunciation. ah-LEE-sha is my preferred pronunciation because I think the three syllable one sounds pretentious and affected.
Alicia and
Alyssa are both decently common names for my age group (I was born in the late 80s). I have heard them on little girls as well, especially
Alyssa, but they don't seem to be quite as common. I think
Alicia is a bit dated, yes.
Out of
Alice,
Alicia and
Alyssa, I'd choose
Alice every time.