these are CC0, so you can use them anywhere you'd like, including in commercial settings where you make money and in your branding. they're not exclusive unless you add your own exclusive edits, and items showing other companies' logos or national flags carry those owners' rules.
no.
the maintainers of vibegif recommend webp. it's actually more quality than gif, because gif is limited in color range (256 colors per frame) and semi-transparency (every pixel is either fully see-through or fully solid), so gradients get banded and soft edges get jagged. every animation here comes in both, so use the .gif only where webp isn't supported.