You seem to be misunderstanding processor with architecture. A processor is hardware component. An architecture is the "machine language" it understands: its set of instructions, registers size, etc.
So, different processors, from different families, can "speak" the same "language", meaning that they understand same binary code and act accordingly. For example, both (ancient) 386 and 486 processors understand i386 code. Pentium introduced some "extensions", like MMX, SSE, etc.
Some processors also understand more than one instruction set, for backwards-compatibility: for example, all modern AMD (and Intel) CPUs are compatible with both i386 and amd64.
A detailed list of architectures (with links to which processors support them) can be found here: http://en.wikipedia.org/wiki/List_of_CPU_architectures
Last but not least, for your last question, the answer would be: yes, you can run 32bit packages in 64bit processors, since most will understand both architectures, as long as your OS is also 32-bit!