I read in the technical paper that new blocks have an empty transaction reserved for the block creator, and that empty transaction is the start of a new coin. If we get 50 coins for creating the new block, where are they (a coin being a chain of transactions)? Are there actually 50 new empty transactions in the new block?
No, as shown by the block linked by PLATO, there's a single 50 BTC generation transaction (which is created ex nihilo as a subsidy for mining and also serves to gradually create and distribute the currency), then the rest of the transactions in the block. Transactions can be of any arbitrary size (down to a current limit of 0.00000001 BTC).
bitcoins aren't exactly like coins in the usual use. effectively, you can cut them into smaller pieces or melt them together into larger ones. a "bitcoin" is basically just a unit of measurement, like an ounce.