[AccessD] Questions on 32-bit 64-bit - Applications Developed with Access-2007

All, 

We are starting to discuss the replacement of a number of old PCs (XP).
They will probably be replaced with new Dell PCs.

We have a number of Access 2007 applications (32 bit).

It is my understanding that Access 2007 applications (32 bit) will run
fine under Win-7 32-bit or Win-7 64 bit.

It is my understanding that there are significant problems when trying
to run Access 2007 (32-bit) applications with Office 2013 (64 bit).  Is
this true?

Also, it is my understanding that if Office 2013 is installed on a
Windows-7 64-bit PC, it will be installed as Office 2013 64-bit.

On the other hand if Office 2013 is installed on a Windows-7 32-bit PC,
it will be installed as Office 2013 32-bit.

Is this correct? 

Will an Access 2007 application run Okay with Office 2013 32-bit?

Thanks,
Brad