Plaster Type Identification and Screw Recommendation

[phloaw]

Hi, I need to fasten standard 15mm water pipes to a division wall in my house (a quite standard terrace house built in UK in the 1970's). Some clips are already in place, but I need to add more (I am talking about clips like this: https://www.wolseley.co.uk/product/center-hinged-wrap-over-pipe-clip-15-mm/)

I am only familiar with brick, cement-plastered walls, so please bear with my newbieness:

1) What kind of wall and plastering do I have? See the pics of a hole in a wall on the same floor:

https://postimg.cc/gallery/2c7gbb97m/

2) What kind of screws (material, size, shape, gauge) do you recommend?

3) Should I use plugs (anchors)? I unmounted one of the existing clips and the screw seems to have none.

Any further advice on what I should/shouldn't do, or anything else, is welcome.

Thanks!