Learn Swedish: Grannen håller ett öga på huset när vi reser. - The neighbour keeps an eye on the house when we travel.

Yes! It translates word-for-word. You use the verb hålla (to hold or keep), ett öga (an eye), and the preposition på (on). It is used exactly like the English expression to mean watching over something.

What happens to the word order if I start the sentence with när vi reser?

Because Swedish strictly follows the V2 rule, the verb must be the second main chunk of information in the main clause. If you start with the subordinate clause när vi reser, the main verb håller must come right after it: När vi reser håller grannen ett öga på huset.

Is it common to say reser bort instead of just reser here?

Very common. Adding the particle bort (away) creates the phrasal verb resa bort, which specifically emphasizes going out of town or going away on a trip, rather than just the general act of travelling. Both work perfectly in this sentence.

What are the past tense forms of the verb håller?

Hålla is an irregular verb that often trips learners up. The present is håller, the past tense is höll, and the supine form (used after have or has) is hållit.