Washing machine waste pipe

Hello all,
Sorry to sound thick...
Without boring you too much: I have recently bought a house and in the process of installing a new washing machine.

The previous w/m waste pipe is connected to the 'u' bend in under the sink...via no less than 3 (yes three!!) 'Extensions'.

Two questions:
(1)Do I 'have' to replace this arrangement in order for my shiny new w/m to function correctly?

and (2) Would it be possible for the waste pipes from the old and new machines to be a different diameter? (the old one is a Servis and the new an Indesit)

Thank you for your time!
Regards, Roy

1. I'd replace it with a properly installed drain system.
2. There could be a variation in the size although it shouldn't be that great.
3. I'd rather have the Servis than the Indesit (not that there's much between them).

Thank you for the advice!-
... I shall connect the waste correctly using the down-pipe!

Regards,
Roy