Hi Heidi. I’d say ‘a key’ as I assume you mean he was one of more than one person who had a key to use at their house. If you say ‘the key’ it means he was the only one using/staying in the house. I’m away for a month so I’ve given my best friend the key to my house so she can live there while I’m away I’m letting my friend stay in my spare bedroom, so I’ve given her a key to my house so she can come in and out whenever she wants (while I’m living there too) Btw do you mean bought or brought?

I think "a" and "the" are equally good. The number of keys doesn't need to play any role in your decision. When I give you a key to my house, I would say "This is THE key to my house ", even though it is only one of many. I say "the" to emphasize its importance, not its uniqueness.

If there's only one key to the house, or if the previously established context is referring to a specific key already, then either option can work fine. But if there are multiple keys and there's no established context referring to a specific key, then use "a".

I would add to Simon's excellent answer that using the Past Continuous tense and the adverb "while" in the initial clause of the first sentence would make the timing of the actions clearer. I would recommend: While Leon was traveling around the world...

Both ‘a’ and ‘the’ could work here. Saying ‘the’ wouldn’t necessarily be inferred to mean that there is only one key. It could also change the meaning of ‘key’ to mean ‘type of key’. Also possible is just ‘their house key(s)’. Using the plural could also mean that you are talking about the keys to different locked things in the house: garage, attic, interior rooms, vehicles etc, not necessarily all of the copies of the keys to the exterior. If it mattered you could be more specific: ‘a copy of the front door key’ for example. What’s a little odd is putting it in the same sentence as ‘making someone tea’ and ‘bringing them food’ which are also somewhat ambiguous but less generous. It kind of comes down to what you are trying to say about the help he received.