Learn German: Dann holt er das Handy, um den Computer zu entsperren. - Then he fetches the cell phone in order to unlock the computer.

The base verb sperren means to lock, block, or bar. The inseparable prefix ent- usually expresses the removal or reversal of a state. By adding it, you get entsperren, which means to remove the lock, or 'to unlock'.

Is entsperren separable? How does that affect the zu in this sentence?

Verbs starting with ent- are always inseparable. When using an inseparable verb in an um ... zu (in order to) clause, the zu sits as a separate word right in front of the infinitive: zu entsperren. If it were a separable verb like aufmachen (to open), the zu would be wedged inside the word: aufzumachen.

Why is the word order Dann holt er instead of 'Dann er holt'?

This is the classic 'verb-second' rule. The adverb Dann takes up the first position in the sentence. The conjugated verb holt must stay in the second position, so the subject er is pushed into the third position.

Is das Handy an English loanword?