Can I assume then that if an aircraft is RNAV-1 able, that it always flies within the parameters required, even when on an RNAV-5 route?
No, the aircraft will fly as accurately as it can, which most of the time is to around 0.02nm accuracy (which is known as ANP or Actual Navigation Performance). The only thing that changes between RNAV-1 and RNAV-5 is how "happy" the aircraft is to be off-track, or how much its ANP can degrade before you'll get flashing amber stuff.
So if, say, the GPS receivers fall offline and ANP gradually rises to 2.0, the aircraft will still happily navigate in RNAV-5 airspace, but not RNAV-1.
Is there any specific training required to be an RNAV-1 pilot or is it assumed if you fly an RNAV-1 aircraft that you are capable of flying within the RNAV-1 parameters?
It's worth mentioning that RNAV-1 is not particularly accurate. That's the RNP we're used to seeing flying SIDs and STARs - most RNAV approaches default to 0.3, and we fly RNP approaches down to 0.1 (required accuracy 10 times that of RNAV-1), which does require specific training.
Second question, how aware are you as a pilot that you are now on an RNAV-1 portion of a route, and would you fly differently?
The current RNP (required nav performance) is displayed on the bottom of the ND on the aircraft I fly, along with the ANP. Nothing changes from oceanic RNP10 airspace to an RNP0.1 approach, except the tolerances involved.
Last question, can you be RNAV-1 compliant and manually flying or does the FMS have to be in full control?
At most RNP values you do have the option of manual flight. We're allowed to hand fly approaches down to RNP 0.3, below that, autopilot use is mandatory.