I noticed that levels didn't seem to raise stats all that much, but I take it that it will actually make a difference?
I did a 11 draw already and got that 5* spear for Kain, but I wanted to save one for whenever Lightning comes around since she's the only character I really want.
As for honing abilities, I haven't been able to survive long enough for me to run out of uses. Except at the boss I guess, but that's because I'm wasting turns healing instead of DPSing.
I'll try grinding some levels and seeing what happens. I take it memory crystals for characters that you get from completing paintings are found in the elite versions of those maps?
For leveling: stats do matter. You will definitly notice the difference once everyone is 50, simply for the fact that everyone will have much more HP (and for long and hard elite fights, you will want bulky characters).
For ability honing: focus on 2* abilities first. When your team is good enough to farm Heroic dungeons, you will want to focus on 3* abilities instead. In any case, some 2* abilities are very good and should be honed to R4 at least, such as Double Cut and Retaliate. Boost is also one of the only 1* ability which you should hone to R4/R5.
For 3* abilities, you will need the Break abilities, especially Power and Magic Break since those are essential to beat some bosses. You will want a R5 Curaga spell too, this one will be helpful for quite a while. Next, you will want to have one 3* Black Magic of each element honed to R3 or R4 (Firaga, Blizzaga, Thundaga, Waterga, eventually Bioga; special mention for Comet, which is non-elemental and very useful against monsters who don't have any weaknesses).
4* abilities may prove difficult to craft and hone. However, you should try to create Protectga (almost necessary for some fights, as damage mitigation becomes mandatory later on) and/or Quake (for farming purpose).
For Memory crystals: yes, those can only be unlocked in the Elite version of an event (with some exceptions: Core Characters's Memory Crystals can be unlocked via regular and Elite paintings, not events).