Bitcoin adress security questions
Transactions use at least one input and one output. The exception being the Coinbase transaction which creates new money and doesn't have an input.

While multiple public keys hash to the same address, there are still 2^160 distinct addresses possible. Therefore the chance that two people generate a private key that resolves to the same address is negligible.

You cannot stop anyone from sending you bitcoins. Receiving bitcoins is entirely passive. The only way to refuse a transaction is by returning it to the sender.