"My friend comes to my house."
Translation:मेरा दोस्त मेरे घर आता है ।
There is an implicit postposition before आता that corresponds to the word 'to' in the English sentence. मेरा दोस्त मेरे घर (को) आता है।
The object of this postposition is 'मेरे घर' which is why it is in the oblique case.
To see why this is the object, look for the part of the sentence that answers the question 'किस को?'/'To what?'. That would be मेरे घर/'my house'.
All the information about the Hindi cases seem to be in Hindi and I'm unable to find an English article. You can google कारक or विभक्ति if you want to try reading them.
The Hindi cases along with their English names, corresponding postpositions (for use with nouns) and the example case forms for the pronoun मैं (I) are as follows:
1. कर्ता (Nominative) - denotes the subject - ने - मैं, मैंने
2. कर्म(Accusative) -indicates the object of the verb - को - मुझे
3. करण (Instrumental) - indicates the means by which an action is done - से, के साथ, के द्वारा - मुझसे, मेरे साथ, मेरे द्वारा
4. संप्रदान (Dative) - indicates the recipient of an action - के लिए, को - मेरे लिए, मुझे
5. अपादान (Ablative) - indicates separation from or comparison- से - मुझसे
6. संबंध (Genitive) - indicates relationships - का, के, की - मेरा, मेरी, मेरे
7. अधिकरण (Locative) - indicates spatial or temporal location- में, पर - मुझमें, मुझपे
8. The eighth case संबोधन (Vocative) is used for directly addressing someone. As a result, it's a little different from the others and does not have a corresponding postposition. For both nouns and pronouns, you can add case markers like अरे, हे etc before them.
You can see that some of the case forms are exactly the same. This is an example of syncretism where multiple cases with different functions converged to a single form over time.
The best way would be to create a new post in the Hindi forums https://forum.duolingo.com/topic/930
मेरे is the plural form of मेरा. Eg: मेरा बेटा = 'my son', मेरे बेटे ='my sons'.
In addition, मेरे is also the oblique-case form of मेरा. It is used when the phrase containing मेरा is the object of a postposition.
For example, मेरे बेटे का घर = 'My son's house'. Here, 'son' is singular. However, since मेरे बेटे is the object of the positposition का, we use the oblique case forms मेरे and बेटे instead of मेरा and बेटा.
In मेरा दोस्त मेरे घर आता है, there is an implicit postposition after घर that corresponds to the 'to' in the English sentence. Since मेरे घर is the object of this postposition, मेरे is in the oblique-case form.
It agrees with 'friend'.
दोस्त is technically a masculine noun. This is why we use मेरा and the verb conjugates as आता.
However, there is no real feminine alternative for दोस्त. सहेली works for a female friend of a woman/girl but sounds odd for a female friend of a man/boy.
So, दोस्त is increasingly also used as a feminine noun too which would make the sentence 'मेरी दोस्त मेरे घर आती है'. This is technically not grammatically correct but common usage nonetheless.
सहेली is a word that has historically been used only among girls/women. It specifically denotes the friendship between two women which is why a man saying 'मेरी सहेली' sounds odd.
सखी is a word borrowed from Sanskrit which is usually used to denote a female friend in old literature. However, it does have romantic connotations when used by a man. It is also quite anachronistic.
That is why दोस्त is today used as a gender-neutral word and used for female friends as well as male ones though it may grammatically be a masculine noun. IMO मेरी दोस्त मेरे घर आती है should have been accepted for this question.