Some questions on installing 125 AMP rated subpanel for 30AMP draw with 10AWG wire
To answer your questions in turn:


Yes, this is A-OK.  The subpanel amp rating is simply a maximum rating, and it's better to have the extra slots and robustness of say a 125A panel vs a 50A one.  (Very small panels tend to be awkwardly laid out, too -- yours, fortunately, doesn't suffer from that infelicity, but that's only one reason to get a 12, 16, or 20 slot one instead of the 4 slot one you have.)
As long as the load on the feeder does not exceed 30A, you're golden.  Use the 3VA/square foot residential Code rule when determining how much actual power is drawn by the general lighting circuits, while I'd borrow the 1500VA/circuit rule from kitchen small appliance circuits for determining how much power the shop circuit uses for load calculation purposes.
The feeder breaker in the upstream subpanel is the disconnecting means for the downstream subpanel in the case of an indoor subpanel like yours.  If you were using a main-breaker panel, you could retain the existing main breaker as an extra disconnecting means, but in a main-lug panel like yours, there's no need to add a disconnecting means that isn't required by the NEC.
Yes, since this is a subpanel, the neutral bar needs to be isolated.  You can remove the bonding strap and screw and chuck them in the trash.  Also, don't forget to get a ground bar kit so that you have a place to hook up grounding wires!
No, it doesn't -- leg balance in split-phase systems is generally taken care of by the way the panelboard's arranged.  You have to install breakers in a pathological fashion (who the heck would skip every other slot in a panel fed with 240V split-phase?!) in order to get a severe unbalance, as the busbars are arranged so adjacent tabs are on opposite legs in most panels.  In the case of your panel -- what you propose (i.e. putting two breakers in one section and the other two in the other) is alright as the inner two tabs are on one leg and the outer two are on the other.