1- Baby pets do not get bigger. They are stuck in eternal cuteness
2- They don't get new skills...never
3- No point...they just gather sp for the heck of it
If you are wondering if they are usefull at this point then I should tell you that for a melee character they come very handy since they make you grind for longer with less downtime. The low lvl heals don't seem much, but since they spam the heal in the long run it adds up very nicely.
On a lvl 40 tank, a baby pet made me possible to grind for an eternity with absolutely no down time.