This is incorrect - while OW removed it as a pan-OW policy, they have now left it up to each airline to define their own guidelines on this, and a number of OW airlines will still check through on separate PNRs - even to other OW airlines - including MH. See here:
Malaysia Airlines Official Policy on Checking bags on separate tickets

Main OW thread:
Bag interlining issues and OW policy changes (Combined threads)

4 flights... I think I remember reading that there is a limit of 3 flights on a single tag (CX only?). However, I have also believe the post mentioned that more than one tag can be used... hopefully someone with experience can chime in. Seems to be 4 sectors can go on one tag, so OP should be fine.[EDIT 2]As OP notes below, MH does max 3 segments on 1 tag (though as mentioned, multiple tags are possible).
(While not MH / OW, I believe this post and the next 2 are relevant: UA Bag Interlining If Separate Tix with *A Partners (YES) & Non *A Partners (NO))

(Yes, MH now uses Amadeus Altea.)