To understand this, you need a SMALL hardware lesson. Intel machines started from an 4-bit environment (the Intel 4004 chip) as a local controller chipset for things like automated washing machines and the like. Programming wasn't so much of a deal. Then came the influx of better miniaturization and the 8 bit (Intel 8008) came out. Then the idea of 16-bit addresses and the Intel 8080 and later, the 8086.
At some point, as miniaturization improved, addresses grew to 32-bit, many years ago. The Intel 80486 and the Pentium (should have been the 80586 - but wasn't) marked the transition to larger and larger memory models. This was also the time when the operating system was switching from MS-DOS to Windows as a layer, followed by Windows as the O/S and DOS as the add-in.
During these transitions, one thing was remarkably constant. Other than the 4004 to 8008 transition, EVERY change in address size and data element size (to match the address size) was matched by an expansion of the instruction set for data sizes of the earlier machines. Therefore, a 486 could run the instructions of the 086. This feature was called BACKWARDS COMPATIBILITY. It has been a goal of Intel and Microsoft to, as much as possible, maintain this compatibility.
With the advent of 64-bit addressing, the SAME THING has happened. The IA64 and related chips can still execute the 32-bit instructions. So it is easy for a program (such as Access/32) to run on a 64-bit machine. All the instructions are there. And Microsoft doesn't make a big thing of it, but a lot of THEIR utilities for 32-bit systems are used unchanged on the 64-bit systems as well. I guess they didn't want to re-invent the wheel yet again.
In your Task Manager, you will see something called SVCHOST, which is the name for a "capsule" in which those 32-bit programs have a comfortable 32-bit environment. Those programs that run under SVCHOST "think" they are on a 32-bit machine and don't know any better. Nor do they know the right questions to ask. (Because if they DID, they would be able to run in 64-bit mode anyway.)
Unfortunately, on the older 32-bit machines, the 64-bit instructions don't exist. So a newer utility such as Access/64 cannot run. Some of the required instructions aren't there and the longer data sizes are not covered by the instructions. SVCHOST won't help because it doesn't support that address size either.
Therefore it is correct to say that a 32-bit app runs in a 64-bit environment, probably in the context of the SVCHOST "encapsulating" utility that provides a shell for execution. But a 64-bit app will not run in a 32-bit-only environment.
To answer your other questions:
1. (Performance effects): IF the 64-bit Office system offsite is running your 32-bit app, see my explanation. The performance will be minimally affected by SVCHOST interactions. It is quite efficient. Kind of HAS to be good because Microsoft uses it for their utilities.
2. (Change nature of app from 32 bit to 64 bit): The status of the app does not change regardless of where you port it. That status will always be the status of the version of Access on which it was developed.
To be brutally honest, we haven't seen many good effects (like higher size limitations) for the Access/64 native implementations. It's one man's opinion and I know why they don't do it, but I doubt MS will EVER do anything to upgrade the capabilities of Access/64 when compared to what they did for Excel/64 - which DID grow in capacity. By a LOT!
The ONLY way to upgrade a 32-bit Access DB to a 64-bit Access DB is to find a machine with Access/64, create a new blank database, and then FROM THE 64-bit Access environment, import the tables from the 32-bit version. (And the other structures!) But that is not generally recommended.