are the websites for libreoffice.org & OpenOffice.org legit?

Yes , they are 100% legit !!
My suggestion is that you go with Libre Office rather than Open Office :D :D

yes, open office is legit, my damn school is using it cuz they don't want to pay
usally, .org are safe

I use OpenOffice myself; LibreOffice, a fork of the same original package, is similar. Either should serve you well.

Yes, they are legit. LibreOffice replaces OpenOffice.org and provides a similar but enhanced and extended Office Suite.

Yes, both are legit.

LibreOffice is the 'no-doubt' FOSS software now maintained by the community. OOo has other licensing issues that could, potentially could, become an encumbrance for royalties used. However, OOo is the more advanced if you build the developer version and with OOo you can program the office suite and use MySql. Oracle has been vague about what the license status is for Java and OOo. Apache is the maintainer now for OOo.