Mundane is a superformat (format applied on top of other formats) intended to reduce the powerlevel and expense of constructed formats without relying on volatile and contradictory information like pricelists.
For the banlists, cards are classified according to the highest rarity printing that appears on Gatherer/Scryfall. This means, for example, that all printings of all cards reprinted in Masterpiece and From the Vault sets are banned. If you want to know if a card is banned, simply search for it and check the rarity of the highest printing.
During deck construction, just use the rarity printed on the legal card to determine what rarity it counts as. This makes decks less cumbersome to construct.
e.g. Force of Will is banned because it was reprinted as a Mythic Rare in Masters 25. Serra Angel is banned because it was reprinted as a Mythic Rare in From the Vault: Angels. Fetchlands, shocklands, etc. are banned because they were printed at Mythic in Zendikar Expeditions.
For the purposes of determining card legality due to bans in other formats, consult the official Magic banned/restricted list, or simply search for the card on Gatherer and check its individual legality in all official formats.
Note: Scryfall includes legality in unofficial formats. 1v1 Commander, Penny Dreadful, etc. are not official WotC formats.
Cards can exempt themselves from the four-of (two-of) rule, but not the rarity distribution or other format restrictions.
e.g. Decks can contain 20% Rat Colony. They are exempted from the two-of restriction, but they each count as commons toward the 20% limit per the "highest printing rule." Contrawise, you may not use Daretti, Scrap Savant as a commander because planeswalkers are banned as a format restriction.
All cards banned in the underlying format are also banned, whether that format is official or unofficial. Mundane only imposes additional restrictions on the underlying format.