I guess you mean something that is first party on both platforms? Otherwise SMS-like communication is obviously a solved issue (Signal/WhatsApp/Messenger et al).
Does Android have something similar to iMessage?
Does Android have something similar to iMessage?
Kind of-ish. The RCS support is rolling out slowly. Of course there is a big difference in that RCS is not end to end encrypted. Also, there is nothing stopping Apple from implementing RCS as well, but I doubt they will do.
If there's one thing that Apple hates more than lost profits, it's handing over control of anything to carriers. Cheap-subscription iMessage/Facetime for Android would strangle RCS/Duo in the cradle and put a thumb in the eye of the carriers, while bringing in some steady and significant regular revenue. Let's not forget that Apple is already offering a subscription service on Android, Apple Music. They're not averse to the concept.
No. The parent to your comment means open iMessage between Android and iOS.