I've not taken it out yet, but here are some weird things I noticed after I sent in my drone for repairs:

1. Before: when stopping the props, I move both joysticks down and in. After: ONLY the left can go down and in
2. When I start up, the gimbal seems to be a bit crooked
3. When I start up (still on the ground), when I move the left joystick right/left, the camera slightly move in those direction.

Can someone explain?

First you stated: 1. Before: when stopping the props, I move both joysticks down and in. After: ONLY the left can go down and in

You should NEVER use CSC to stop the motors. Always use left stick down. Stopping with CSC can cause a flip over and damage.

Second you stated: 2. When I start up, the gimbal seems to be a bit crooked
This could be normal, unable to tell without photo's.

Third you stated:   3. When I start up (still on the ground), when I move the left joystick right/left, the camera slightly move in those direction.
This is normal, but again inadvisable to do

Just my 2 cents worth.

Not exactly sure what you are saying about the left stick only, but I think the following info will answer your question.  Pulling both sticks down and in (known as a CSC) will stop the motors, but it is only intended as an emergency stop if you are in the air.  If you have the latest firmware they increased the time it would take to activate to 3 seconds.  You might think down and inwards isn't working at all now, but it still does.  In any case, when you land and want to shut the motors off, just pull the left stick down and hold it, the motors will shut off safely.  Before you ask, you can pull the left stick down and hold it while it is in flight and it will not turn off the motors.  It only works when it detects the aircraft isn't descending.  Any combination of left stick down and in or out will still register as left stick down and stop.  If you do a CSC on the ground there is a real possibility the aircraft can flip and damage itself.  Don't use CSC unless there is an emergency in the air, just use the left stick to stop the motors.  You still use the CSC to start them, or use the on-screen controls.  Don't worry about what is in the manual, it isn't written well and has been changed and updated in later versions.

Some people have reported crooked gimbals/cameras, you would need to post a picture to see what is going on.  Sometimes the gimbal becomes loose on the shaft and can be adjusted and tightened in the proper orientation.

When you move the joystick on the ground you will see the camera move slightly left and right.  This is normal, the camera needs to move a bit to take any shake out of the picture as it is rotating, and keep the image smooth and stabilized.  This is nothing to worry about.  It cannot pan left or right (you rotate the aircraft to get that shot) but the gimbal does need to move sideways by itself for stability.

I would concur that it would be helpful to get a visual in order to see the extent of the gimbal tilt. Is this after performing a gimbal calibration or a IMU/gimbal calibration combo? Just to clarify, do you mean that the motors will only stopp when the left stick is in the down-in position and not both sticks, or does the right stick literally not move at all? For the last question, some twitching can occurr when performing a rudder command  since the gimbal wants to follow the aircraft in that direction in order to stay center.