Is it normal in German to use Schuh in singular in this context? (I would use the singular form only if I was looking for my left shoe, for example.)
No, it's not normal in German. As you said, in most real-life situations, you would use the plural. The sentence is grammatically correct though and - theoretically - there might be situations in which you would use the singular. E.g. if a little girl is playing with one of your shoes.
Thanks for your answer. One of the shortcomings of Duo is using grammatically correct learning sentences which are not very plausible. If it takes a exaggerated hypothetical situation to justify its usage, then it would be better to use a more reasonable construction. Like, in this case, Jacke, Mantel, Hemd, Haus, etc. Or, using the plural.
If it was Schuhe instead of Schuh would you use deine instead of deinen because it's plural?
Yes, "The girl likes your shoes" = "Das Mädchen mag deine Schuhe" (plural accusative).
So why, if they say Schuh is "shoe" or "boot", is "The girl likes your boot" incorrect?
Like the articles, the possessive determiners (my, your, his, etc.) agree in gender/number (masculine, feminine, neuter OR plural) and case with the noun they refer to. In this sentence, "your" refers to "shoe" (Schuh), which is:
2) accusative (it's the direct object and almost all direct objects are in the accusative case)
The ending for masculine accusative possessive determiners is -en: deinen. See this table (it's for "my", but the endings are the same):
oh that makes sense now! thank you for the chart, i wish that duo explained it this way
Would 'the girls like your shoe' be the same? since girls like and girl likes would both be Mädchen mag, they would, right?
Was marked incorrect for "Das Mädchen mag ihren Schuh". If I was addressing this in the formal sense then what is the answer if not "ihren Schuh"?