My personal feelings (I'm not a sparky):
1) Yes, get a qualified engineer to change the socket and check the cable inside the wall at the same time.
2) No need to change the flex. Judging by kingdech's photo 7 at 1:39 p.m. on Sunday, the flex is reasonably long. So cut the flex a few inches from the plug and then use a new good quality (as JohnD said at 1:55 p.m. on Sunday) plug.
1) Yes, get a qualified engineer to change the socket and check the cable inside the wall at the same time.
2) No need to change the flex. Judging by kingdech's photo 7 at 1:39 p.m. on Sunday, the flex is reasonably long. So cut the flex a few inches from the plug and then use a new good quality (as JohnD said at 1:55 p.m. on Sunday) plug.