Yes, you can continue to use RS 15.7.1 (and ASE 15.7 for the RSSD) for replicating between ASE 16 databases. If you're using a (relatively) old version of RS 15.7.1 then the ASE 16 repagents should limit themselves to a LTL version supported by the repserver (the ASE 16 errorlog will display messages - when the repagent connects to the repserver - with details about the LTL levels in use by repagent and repserver).
Yes, ASE 16 can act as the host for the RS 15.7.1 repserver's RSSD. Again, if using a relatively old version of RS 15.7.1, a RSSD repagent (if configured) should limit itself to the LTL version supported by the repserver.
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As for upgrading ...
You could either:
1 - perform an in-place upgrade of the ASE 15.7 dataserver on host_2
or
2 - create a separate/new ASE 16 dataserver on host_2, and then dump-n-load db's from ASE 15.7 to ASE 16
From your proposed steps it sounds like you're looking at option #2.
Obviously (?) you'll want to stop the repagent(s) and shutdown the repserver before dumping/loading the RSSD into the ASE 16 dataserver, then configure the repserver (and it's interfaces file) to point at the ASE 16 dataserver, then once the RSSD dbdump has been loaded and onlined in the ASE 16 dataserver, start up the repserver so it accesses the ASE 16 dataserver, then start the repagent(s).
Where it gets a little tricky is if you choose to call the ASE 16 dataserver by a different name, or give the ASE 16 RSSD database a different name ... as then you'll need to make some changes to the rs_* tables in the (ASE 16) RSSD database ... update the repserver's *cfg file ... reconfigure the repagents ... plus update the ID server's rs_idnames table with the new name of the RSSD dataserver/database.
Ideally the new ASE 16 dataserver will have the same name as the ASE 15 dataserver it's replacing.
While both dataservers can remain up and running at the same time they will need to be listening on different ports ... which in turn means you'll need to make sure all interfaces/sql.ini files in the replication domain are referencing the port# of the new ASE 16 dataserver.
On other other hand, if you'll be shutting down the ASE 15 dataserver before starting the ASE 16 dataserver, and the ASE 16 dataserver will be using the same port# as the ASE 15 dataserver, then you shouldn't need to modify any interfaces/sql.ini files.
Net result is that what you propose is doable, but you'll need to think through the ramifications for any users and/or applications (including repserver) that connect to the dataserver on host_2 ... and then pay careful attention to the details.