Hi Ciaren, thanks for reaching out! I didn't realise my blog was mentioned in TSR, that's nice to know. Don't suppose you have a link? (just curious! :-))
I was actually at the City Uni alumni meetup just yesterday, giving a talk to the current students about life after MSc. I'll probably be back for more meetups, so we might see each other in person then.
I have done the course full time, but lots of my fellow students have done it part time quite successfully. It's an intense course, so be prepared to sign your life away. Two days per week + weekends is a decent allowance, I think you should be fine.
Any MSc student could do an internship, no matter whether full or part time. However, the department doesn't hand hold you with this. They might advertise a few places through contacts, but you will be expected to interview competitively for them and to have a portfolio ready. You are also free to source your own internship (I think quite a lot of students have done this). Having said all that, I didn't do an internship because I felt that would be too much pressure, and it's not necessary to find successful employment (although I suspect it helps).
Jobwise, yes, UX is competitive. However, City grads do stand out because they have highly original and interesting portfolios compared to, say, bootcamp grads, and have familiarity with a wide range of subjects and research frameworks. But it helps to have some real world projects, too. There will be some in the course itself (like working with charities to improve their website usability), but you could look for other projects (through Upwork, for example, or through friends/family).
Hope this helps, and best of luck!