"The wife has an aged husband."
Translation:Uxor maritum senilem habet.
It definitely does! It's far more fluid than English for certain, but there are preferred word orders which in certain sentences can dictate where things have to go. For instance, when asking a yes or no question, the verb will virtually always be first. In other scenarios, the verb will usually be at the end of the clause to which it refers, as the general rule of thumb is SOV for word order.
The adjective vetus is 3rd declension, so the accusative is veterem, not vetum.
“vetum” assumes that “vetus” is second declension. vetus is actually third declension, as inconcinna has stated, and we have to obey the third declension rules. The stem of “vetus” is “veter”, to which is added third declension endings, except in the nominative singular, where all genders in this instance are “vetus”, and the neuter singular accusative, which is also “vetus”.