Gearbox first gear
 

Hi when i put the first gear I have the impression that something moves in the gearbox, it's normal ?

Are you referring to the loud thump that can occur when going into first gear? What makes you think that something moves in the gearbox?

Big plastic snap ring that holds shifter boot down come detached?

It's not noisy ;)
Ok so engine off and cold, all gears pass smooth.
But when i drive the car, for exemple i arrive at a red light => down shift, down shift and when i'm slow in 2nd, I put the first gear when i'm at 0, it's at this moment. When the first gear is half engaged, it feels like a little struggle and if i finish to engage the first gear I feel that I push something in the gearbox

When engaging first gear when the car isn't moving you will usually feel a slight "clunk". This is normal, and is quite noticeable when the engine is cold.

If you're having trouble downshifting into first when coasting to a stop, try double clutching (put it in neutral, take your foot off the clutch, then press on the clutch pedal and put it into first). But don't try to put it in gear if you're still rolling.