Yes. Let's calculate the minimum size of a block:

• The block header must be exactly 80 bytes. This is the only part of the block that miners actually mine; the rest of the block is data that the header securely references.

• The transaction count. This isn't part of the block header and it isn't part of the block data, but it's part of the peer-to-peer protocol block message so it gets counted towards the block size. For blocks with 253 or fewer transactions, this is 1 byte.

• The coinbase transaction, the only required transaction in a block. The coinbase transaction has the following fields with these minimum values:

  • 4 bytes -- version field
  • 1 byte -- number of inputs (always 1 for coinbase transactions)
  • 32 bytes -- outpoint txid; always 32 0x00 bytes for coinbase transactions
  • 4 bytes -- outpoint index; always 4 0xff bytes for coinbase transactions
  • 1 byte -- number of bytes in coinbase field (input script); always 1 byte for coinbase transactions because there's a 100-byte limit
  • 4 bytes -- block height as a data push; required by BIP34
  • 4 bytes -- sequence number
  • 1 byte -- number of outputs, we're not going to have any (making the block reward and transaction fees paid in this block permanently unspendable; no real miner would do this)
  • 4 bytes -- locktime
  • Total: 55 bytes

Total minimum block size: 80 + 1 + 55 = 136 bytes

Practically, the smallest reasonable blocks are in the 180-byte range.

Sure.

This is one such block. It's 312 kB.

Blocks have to have at least one transaction: They must contain a coinbase which is the transaction that spends the block reward.

For example this block with only one transaction is only 0.246 kB.