Question about UTXO and indivisibility
A Satoshi is the smallest unit of account within the Bitcoin network that can be transacted. One BTC equals 100,000,000 Satoshis.

The 0.1 BTC in your example is 10,000,000 Satoshis. 5,000,000 Satoshis are applied the that special person in its own UTXO, and 5,000,000 Satoshis minus mining fees are sent back to yourself to another address, and is recorded as another unspent transaction output (UTXO). 

A UTXO is defined by a transaction's ID and the output index of that transaction.  For each successful transaction whose outputs are unspent, each output is a UTXO. An additional point is UTXOs are atomic in the sense all of a UTXO's balance is spent or none of a UTXO gets spent in a transaction.

FYSA - In the future, we might see the term UTXO deprecated with the term called payment.