Im no tech-spert but I do have a Baby Gaggia.
Im not sure what grind fineness youre getting, but I find if the coffee is clumping slightly and feels very fine not gritty between your fingers then you should be OK.
The water trickling back into the water tank is just your three way solenoid valve. When the pressure gets too high the solenoid valve diverts water back into the tank, preventing the pressure created by the pump getting too high. Every time I make coffee the over pressure water is directed back to the tank. If it wasnt happening Id think you would be getting a fairly fast underextracted pour. Resistance is good :)
There is usually a delay of about 8 seconds, and as much as 12 before I fear the grind is too fine and Ive gone beyond a ristretto style pour. So dont give up if the pour is delayed and then slow. As long as you are getting approximately 20-30mls in anywhere between 20 and 30 seconds,for a single shot and double the volume (40-60mls) for a double,in the same sort of time, then you are OK.
Dosing tends to make a difference too. If you have your basket as full as possible then extraction will be slower than an under dosed basket.
Keep your tamping at the same pressure and try adjusting your grind a bit and see how you go. There could be something physically wrong with your machine, but try a few things before pulling it apart :)