Yes, Oracle XE is free and you may download deploy and distribute it freely. Please see section "Oracle Database Express Edition" from link:
You may download windows 32 bit, and i am afraid 64 bit is not available.
Hope this helps!
If this is a standalone machine for DB only, then there is no point you going for a windows 64bit and I suggest you stick to 32 bit as, Oracle Express Edition will only support 4GB memory and there is no advantage you going to windows 64bit as 64bit OS is used to support memory capacity above 4GB.
are you telling me that I can install oracle express edition 32 bit on a 64 bit windows machine?
According to Oracel, you will have to have 32 bit OS running and 32 bit XE running.
But I personally have had experiences installing 32bit clients on 64bit OS and running without a problem. You may give a try, but I cant guarantee you it will work for sure.