<p>I think “to” can and should be omitted from the last one. The idea is that each time you list something, you’re leaving preceding parts of the sentence implicit. For example:</p>
<p>I like to ski, hike, take pictures and run . . . </p>
<p>. . . is really saying . . .</p>
<p>I like to ski, I like to take pictures, and I like to run . . .</p>
<p>But of course, you don’t say that. What lets you leave those parts omitted is that they’re all the same.</p>
<p>I like to ski, I like to take pictures, and I like to run . . .</p>
<p>But if the sentence (in its “explicit” form) were . . .</p>
<p>I like to ski, I like to take pictures, and Barry White is off the hook</p>
<p>. . . you couldn’t rewrite it at all. There are no parts in common in each listed item.</p>
<p>Now, looking at your fourth example:</p>
<p>Her parents objected to the loud music she played and her parents objected to the late hours she kept</p>
<p>Both pieces have “her parents objected to” and so that phrase can be, and should be, omitted from the second item. </p>
<p>Her parents objected to the loud music she played and the late hours she kept.</p>
<p>(Just as an aside, you can never omit articles like this. “The” always needs to be there.)</p>