That's very helpful, Horseshoes.
Chimney: If the other sides are as good as that, then certainly no mass re-pointing necessary. It looks fine to me.
It's a halfbrick thick. Approx 4".... so, It's much more likely to be rain penetration. When modern chimneys are built, a sheet of lead is laid through the thickness of the stack (with a hole for the flue(s).) This carries any penetration back outside. In an old stack, this may be absent, or failed. Re-building is the only option here.
Render: I guess they didn't stipulate a lime render? It does look like rather too strong sand & cement - hence the cracking. Lime is more trouble to apply, but far more forgiving, and self-repairing.
Is it facing West? If so, West plus Wales means a lot of attack from the weather. It's important to remember that, with the last few months weather, builders and particularly roofers, are seeing perfectly sound masonry and roofs that have been completely overloaded by storm driven rain. Not with newer houses (better back-up precautions are taken now), but with older properties.
Without going into major renovations/rebuilding etc, this type of product is excellent............
http://www.screwfix.com/p/thompson-s-water-seal/52043
Don't be put off by the purists. A silicone waterproofer will not be detrimental to the masonry or the chimney. The building will "breathe" quite adequately from the inside
It would be nice to rebuild and re-render, but, sometimes, needs must.
Fill the cracks and apply a couple of coats, especially the chimney. Easy, quick job with a brush or roller. Only needs to be re-done at next decorating time.