"My mother loves my father."
This is a massive headache. It was more common to refer to one's parents or elder siblings politely in the past, in a more Confucian order to society. Children would never refer to their mother as 私の母 -- the 私の is totally unnecessary there. Climbing the family tree you might though -- to distinguish between the children's mother (家の母) and the parent who is speaking. And then there's the problem that usually 私の母は父~ usually means my mother ~ her father. So, um, don't use this unless you're sure they already know what you're talking about?
"母は父を好き" 36 700
"母は父が愛" none (but one for "母は父が愛し")
I translated it as 母は私の父を愛しています because of exactly your point. You don't need 私の for 母 because my mother is the assumed translation. But Duolingo says it's wrong to refer the my father as 私の父, even though to not say that would make the sentence even more confusing.
Duolingo says it's wrong though, but I don't think so.
It is confusing, (and seems quite arbitrary) when you require the topic わたしは in the answer to some questions, but not all. It would be helpful if the sentence structures were more consistent.
Duolingo does not teach learners that it is sometimes unnecessary to include the topic in Japanese (as it is understood).
This one is confusing me on word order. I would have read the answer Duo gives as meaning "Speaking of my mother, my father loves her."
[FWIW, I had the same problem years ago learning Latin. I could get the vocabulary. But I could never figure out if Spot caught the ball, of if the ball caught Spot. ]
This point has already been made by IsolaCiao, but just to reinforce it, when you are speaking Japanese (at least in my experience) NO ONE actually using the word あいしてる, it is much more natural to say だいすき in this scenario because the word "あいしてる" is SUPER strong in Japanese. Yes it technically means "love" but this is the type of love that like your grandfather tells your grandmother as his final words on his deathbed to her type ❤❤❤❤, NO ONE is using this word for everyday speak.
Check the top comment on this thread: https://forum.duolingo.com/comment/25687448/%E3%81%97%E3%81%A6%E3%81%BE%E3%81%99-vs-%E3%81%97%E3%81%BE%E3%81%99
In short, "します" indicates a habitual or future action. テニスをします。means "I play tennis" or "I will play tennis", where テニスをしています means "I am playing tennis".
In this instance, I'd take the している form to mean, "My mother loves my father"; not occasionally, or in the future, but presently and continuously. Really, the confusion here is English's idea of "the present". There are 4 different present tenses in English: simple present, present perfect, present continuous, and present perfect continuous, and these don't always map 1-to-1 into Japanese.
There's nuance to this, and I still get confused by different examples / scenarios. E.g. what's the semantic difference between "I worked at that company" and "I was working at that company"? (I actually don't know). And things like "The sky is clear", is 空が晴れています (sora ga hareteimasu); ています is used because the sentence really means "the sky is in the state of being clear". But then how would you say "The sky is clearing?" I.e. It's not clear yet but it is becoming clear.