Zach1928, welcome to the forums.
The windows.old folder can safely be deleted, Windows.old Folder - Delete
might want to go through it just in case you missed backing up anything before deleting it.
As for the Program Files (x86) folder, delete that and you're looking at repairing or re-install Windows. That is where 32 bit programs get installed as well as any and all 32 bit Windows components, including 32 bit version Internet Explorer. The Program Files folder is for 64 bit applications. The reason for the two of them is to separate the 32 bit from the 64 bit programs.
Same thing goes for the System32 folder and the SysWOW64 folder. Despite its name the System32 folder is where the 64 bit system files are to be found, and the SysWOW64 folder is where the 32 bit versions are.