The spring clips on the calipers are known as anti-rattle clips. That's their only function in life, to stop the rattle of the floating caliper against the fixed portion.
Driving w/o causes no harm but can be annoying when driving over uneven roads, especially cobblestones. You should replace these to make sure you get even pad break-in and wear.
As far as the pedal goes, I think the shop didn't bleed the brakes properly and let some air in causing the spongy feeling. This feeling can also be caused if the shop just simply pushed the piston back w/o doing a brake flush.
