It is possible to play tunes, but it takes a great deal of practice. Pretend it's a fretless guitar, and listen really, really hard.
Warm soapy water is the best thing for Bakelite, provided there are no cracks. I'd be tempted to just wipe it with a damp cloth. Any grease on it will be a result of handling, and will either wear off or shine up with more handling.
Thread Creep - all the Clangers' episodes were scripted, and there was an uproar at the BBC when Mr Postgate wanted to start with a particular phrase. The BBC argued that you couldn't say that sort of thing on Children's TV, and Mr Postgate argued that it was what the Clanger would say. The argument was won by someone else pointing out that as it was being done entirely by whistles, the odds on someone understanding what they were actually saying was infintesimally small.
That phrase uttered by Major Clanger - clearly understood by myself and several others - 'Oh sod it, the damn thing's stuck again!'