Q1) Do you think such inrush current may damage the LP3982?
A1) I don't think the current is actually through the LP3982 unless you measured current into the Vin pin. Not sure where you measured the input current, but based on polarity I'll guess you measured near the USB connector (red wire?) closest to the PCB. If that's the case then this is likely inductive kickback from the USB cable and the inital charging of the input capacitor coming to an end. But with USB cable power using a twisted pair I am surprised to see an ampltude this high.
Q2) If so, Do you know non expensive way to lower the inrush current?
A2) Typically a low value series resistor between the USB connector and Cin will provide damping. Essentially a low pass RC filter. Ferrite bead could be another option.
Q3) As you can see in the picture waveform2.png there is some ringing (transient) at the LP3982 output, is this normal?
A3) If this right at the time where Vin is initially applied, this is generally typical but is not due to the LDO as Vin is not high enough for the LDO to be operational. Ideally you would like to have a smoother start-up on the input. to reduce this.
Q4) I also make a stress test by connecting the PCB to my laptop laike 20 times, at the end the output voltage was still around 3.2V. Do you think I could have a problem in the future?
A4) Unknown. 20x on one USB port is not a very substantial sample size, unless this will only be connected to your laptop. The dynamics of the USB ports, and possibly the USB cable, could be a substantial variable out in the rest of the world.