Anytime Day Return tickets are valid for one return journey. The outward portion is valid on the date shown on the ticket and until 04:29 the following morning.
Instead of multiple itineraries and airlines, a round-trip may just make your life easier if you don't want to deal with more than one reservation at a time. In addition, two different reservations could become a hassle if one flight delay or cancellation on the outbound forces you to cancel or change the return trip.
Proof of onward travel means that airlines and governments want to make sure you are not illegally immigrating to their country, so they need to see proof of a return ticket home. Basically, some countries want to make sure you aren't attempting to move there on a tourist visa and never leave.
In general, you will have to use all flight segments in your ticket in the order you booked them. You are not forced to use the return portion of your ticket if you decide not to go home, but you are not allowed only to use the return flight and skip the departure flight.
Proof of onward travel means that airlines and governments want to make sure you are not illegally immigrating to their country, so they need to see proof of a return ticket home. Basically, some countries want to make sure you aren't attempting to move there on a tourist visa and never leave.