1. Yes, OpenOffice will load and run on Windows 8. If you have problems installing it these are easily solved - post back here for help if needed.
2. I have no knowledge of One Note, so cannot advise on something similar. There is nothing integral with OpenOffice, but there may be suitable programs which integrate.
Apache OpenOffice 4.1.2 on Xubuntu 15.10 (mostly 64 bit version) and infrequently on Win2K/XP