on your 64 bit Windows 7 and the 32 bit browser will run just fine.
Your remark "As always, IE closes unexpectedly" needs some clarification as the problem might well be caused by malware running on the PC because IE does not normally close unexpectedly.
I have windows 7 (premium) with IE 8. As always, IE closes unexpectedly. I have had firefox and do not like newest. Can I install Chrome on win 7 64 bit? Any suggestions on this or other stable browsers?