2. The Pink (Magenta- as Boeing calls it ) bug is the HDG bug from the Mode Control Panel (MCP). ie in picture 4 the HDG bug (top left) reads 132 on the MCP and would read this on the ND and PFD.
In pic 3 it reads 118 on the PFD therefore would read 118 on the MCP, spin the HDG bug on the MCP and the the Magenta bugs will follow it on the ND/PFD. It is unrelated to the FMC ie raw data.
The Magenta lines are what the FMC is programmed to follow while in LNAV (if I remember correctly they are actually Great circle routes between waypoints), the Magenta HDG bug would be followed if in HDG SEL ie inverted triangle over Magenta hdg bug.
The long thin white line is actual A/C track and should lay over/under the magenta line when on track. ( BA use HDG up instead of TRK up therfore pic 3 ND would be rotated approx 3 degrees left with HDG 111 MAG displayed at the top).
The turbulence as you said probably caused it to go off track and the A/P is making a correction to return to track, you can see how far off track you are on the FMC(not shown) ie. R 0.2nm
Hope this helps.