1) Motherwell and Uddingston skipping Bellshill
Plenty of trains do this, although most do not call at Uddingston. The 2-hourly service from Glasgow Central to Edinburgh via Carstairs runs on this route (which is the WCML "proper", and is the route you'll take if you take Virgin Trains to London for example).
In the old days before the timetable recast, there were rush hour trains running non-stop Argyle Street to Motherwell (perhaps calling at Rutherglen?) and onto Lanark, but these aren't quite as common now that the timetable is much more regular and the Lanark trains already benefit from faster journey times by virtue of running into the High Level.
2) Motherwell (Shieldmuir) and Carluke skipping Wishaw
Why would they want to avoid Wishaw? It's a significant detour, but it's also a major centre of population, with a well used railway station serving 400,000 passengers per year and having the highest usage figures of any Argyle Line station South of Motherwell. It may save time to avoid Wishaw, but it's a big enough settlement that the train warrants calling there.
The only reason why they would not call is if it makes more operational sense not to - and in the case of the 15:49 EDB-GLC, it's followed through Carluke by a local service that subsequently does call at Motherwell and Shieldmuir so there's no point in the faster Edinburgh to Glasgow train crawling around the deviation.
Interestingly, the Argyle Line now features trains that avoid Motherwell. They run Uddingston-Bellshill-Holytown-Wishaw. Holytown lost 1tph in the recast, and a few rush hour trains now go this way. Previously, all trains would go through Motherwell even if they took a convoluted route in doing so (like the hourly Lanark-Wishaw-Holytown-Motherwell-Hamilton-Glasgow...). It would therefore be appropriate to say that Holytown-Motherwell and Holytown-Wishaw have "limited service", but this hasn't appeared on the map to date. The image posted above almost suggests that there are regular trains between Motherwell and Holytown, and between Holytown and Wishaw, but this is no longer the case.
The lines on the map are actually historical (and can be seen even on the old
SPT maps). They are still accurate, but perhaps the map could do with a minor revamp to reflect the current Argyle line service pattern.