I have a project for school, and I only have PowerPoint 2016, but the computer at my school only has a pretty old version of LibreOffice, how can I ensure my transitions, themes, and fonts will be compatible?
Until you get them to update LO, you can use LO Portable from http://portableapps.com/apps/office/libreoffice_portable since latest LO has improved support for formats than previous version.
If you can afford to release files to improve support, make a bug report at https://bugs.documentfoundation.org/enter_bug.cgi with the files attached, with precise screenshots and instructions and LO will be improved once again.
Likely only with some difficulty. It may not even be possible. Keep all styling and transitions as simple as possible. You may also need to avoid using a theme defined in MSO 2016 and instead create a basic master page the elements of which are supported by PPT/X and both products. Bridging large version+product gaps is always a challenge.