32 or 64 bit kernel for Duo T8400 processor ? Can apps be 32 bit for 64 bit kernel ?

[linuxguy]

My new laptop has an Intel Duo T8400 processor.  Should I install the 32
or 64 bit distro ?   I run a lot of esoteric open source apps.   Can I
run a 32 bit application if I install the 64 bit distro ?

Thanks