Yes, yes and yes 
May take more than one visit, especially if they send an engineer to look for a call problem, as they are not allowed to touch the cab, but if Broadband Engineer, then they can open cab and have a look.
Engineers bring equipment (or did) that check the line and how well it is performing, joints in the cabinet can become dry and be less conductive.
Some houses, homes, have two pairs of twisted pairs wires (2 sets of wires) so if one set is faulty, engineer can swap broadband over to the second pair for a better quality signal, saves digging up entire Street cable run.
Also in the cabinets are what are known as Line cards, which our Broadband lines connects to, these can also be faulty and they can be swapped / moved etc. (simple version).
In a completely sane world, madness is the only freedom (J.G.Ballard).
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