Both of them would be processed in the next block.
They won't. A block cannot contain conflicting transactions. Only one of the transactions would make it into the next block (typically, whichever transaction happened to reach the miner first), at which point it is said to be "confirmed". Transactions that have not yet been included in a block are "unconfirmed" and merchants should be wary of unconfirmed transactions for exactly this reason.
1) Would the transaction be visible on explorer site ? Both of them ?
Many block explorers will indeed show both unconfirmed transactions, and also a warning that they are in conflict.
2) I get that maybe a few blocks later, the longest chain would be taken and one of the transactions
would be revoked. But how is this reliable at all? The two cars are probably in possession of Alice and Bob already.
As explained, that is not how it works, and in any case the seller would be advised to wait for the transaction to be confirmed before handing over the keys.
The seller needs to wait at least 4 blocks after the transaction is complete?
If he/she likes. This is what is meant by waiting for multiple confirmations, and provides extra security against chain reorganisation (which is what happens when a longer chain suddenly appears out of nowhere, typically due to a temporary split in network topology). The new chain may contain different transactions, so previously confirmed transactions can become unconfirmed again. Chain reorganisations longer than 1 or 2 blocks are extremely rare, however, for very high value transactions it doesn't hurt to be extra cautious.
Also, regarding the 1st question, what happens on the explorer when the longest chain is taken ?
Before longest chain is picked, which one is displayed?
Block explorers display whatever is currently the longest chain known to them. If a longer chain suddenly appears in a chain reorg, block explorers will switch to it immediately.