Isn't that the camera has progressive chip but when record to tape it will split the frame into interlace?

When directly to HDMI or HD-SDI, isn't it will capture what the progressive chip recorded? So, through HDMI live capture of V1, it will be 1920x1980p whether 25p(in PAL) or 30p(in NTSC)

I just want to know if my understanding is the correct ones...

I have a treatment of having a lot of camera movement, not really run n' gun per se. Since the cable can withstand 50ft(15 meter) or 12ft(3.5 meter) as Alex Raskin mentioned, do you think that handheld, with a lot of camera movement, in confined place or limited range of space (limited to the cable length) will be able to suit my treatment.

I never capture live with cable before, I just want to make sure I'm able to do it, since I have an understanding that GOP will suffer badly when doing a lot of camera movement.

No. The camera does have progressive chips, but that's where it ends. As it has been pointed out by others, according to Sony for compatibility the signal is changed to interlace before any output. Therefore, you cannot get native 1080p out of this camera. But that doesn't matter because with the pulldown, you are still getting true progressive in either 24 or 30 frames or 25 frames in PAL land. The only advantage of taking the live HDMI signal is bypassing HDV compression, getting uncompressed images and 4:2:2 color. There are very few cameras, including higher end professional cameras, that will output and/or record 1080p 60.