"She likes to run for half an hour every day."
I'd learn more and faster if I could play the audio of this correct answer. Hearing it aloud would help me figure out what I got wrong more easily. Maybe it's me, and I simply haven't figured out how to play the audio for right answers? If so, please advise. Many thanks!
That's the natural place for 每天 or any other expression of the time when something happens. Putting it at the start of the sentence is allowed, but I think that's just topicalization, not anything special to time particularly.
Duolingo even accepts 她喜欢每天跑半个小时的步 for those of us who really have to make it clear that it's the running that is every day, not just the liking. Again, natural spot is right before the verb.
These are separable verbs (also called verb object phrases). You can typically identify them when the first character indicates an action and the second character indicates a noun. For example in 跑步, 跑 is actually the verb "to run" while 步 is a noun meaning "a step" as in a step in a process.
Modifiers should come after the verb word, and therefore are usually placed between the two characters that make up a separable word. These modifiers are typically auxiliary words like “着 (zhe), 了(le), 过(guò) and quantifiers as we see in this case with the quantifier “半个小时".
It is correct to say 我每天喜欢游泳 since there are no modifiers in your sentence. However if you wanted to say I swam for an hour then 我游了一个小时泳 would be correct. Note the verb modifiers come after the verb word which in this case is 游.
more on separable verbs: https://resources.allsetlearning.com/chinese/grammar/Separable_verb list of separable verbs: https://resources.allsetlearning.com/chinese/grammar/List_of_separable_verbs
You usually can't go wrong with subject-first. In my experience you can often swap subject and time words as well, without changing the meaning of the sentence.
So in this case "她每天喜欢跑半个小时的步" would probably work fine, though I haven't tested to see if Duo accepts it.