Icon licences
Open-source icon sets use software licences: MIT, Apache 2.0, ISC or the SIL Open Font License. All allow commercial use in apps and websites. MIT, Apache and ISC ask you to keep the licence notice with copies you distribute, which for a website or app usually means listing the set in your open-source notices. A few sets are CC BY and need a visible credit.
SVG or PNG
SVG is a vector format: it scales to any size, stays sharp on every screen and can be recoloured with CSS. Use it for icons and logos-style graphics. PNG is a bitmap: pick it for cut-out photos with a transparent background, at the size you'll show them.