Wax and ONO have announced their intentions to launch their projects on sidechains rather than the main chain. Does this mean that they would need their own block producers or are sidechains also supported by the same block producers as EOS?
Yes they will need their own Block Producers to run the sidechain, however, should be able to perform cross chain communication one day so in theory, the side chain can communicate with the main chain.
Scalability is the main problem that any blockchain project aim to resolve. Some separate the process of produce new block of mainchain and sidechain while some does not.
EOS has 21 active BPs to do that at one timestamp and both sidechain and mainchan are processed by them.