Any question answered...

Laxative.

Bent bit of coathanger, cut off with your Park Tools cable cutter and drag out the gunk. Vile job, did it yesterday......

my mate phil says:

*"followed by caustic soda crystals

relatively dangerous bit:
eye and breathing masks and marigolds on, pour a mugful into the sinkhole and leave for 5 minutes. it'll fizz and start to heat up and produce toxic vapours.

realistically very dangerous bit, but effective:
return with a litre jug of just boiled water, double check your protective gear, and pour into the sink in one go. retreat.

once the reaction dies down, flush through with two sink bowl fulls of cold water

if caustic gets on surfaces or clothes it produces a soapy highly corrosive film, thoroughly wipe down any contaminated surfaces, still wearing your protective gear. put any contaminated clothes immediately into a cold wash or cold water bucket. if you get some on your skin, flush under cold water only for 5 minutes, there may still be chemical burning and scarring afterwards. if in the eye, flush under cold water and call an ambulance"*

he's a chemist, therefore a bit of a chancer though..

the quote function for tracts of text is shite

This stuff. There is a bathroom version as well.

As per previous re caustic soda but if you can access the P trap then you can probably sort the problem out and then put the caustic through it's once back together. In my kids' bathroom it is my daughter's long hair which seems to clog it.

Drainbuster. Doesn't do what it says on the tin - it unblocks drains, does not bust them.