Depends a bit if you consider two items connected by "or" an enumeration, which usually requires an "and", but "or" can be satisfied by having either one alternative satisfied, or both, so it can also refer to the two months, thus necessitating the plural. "is" is logically a bit sloppy, and to mark "are" as wrong, is simply wrong. Some context would have been helpful, and if it would have concentrated on a choice ("either / or"), "How about" would make it a lot clearer.
It would, in a conversational context: "When can we go on holiday?" "How is [=about] September or October?" Since those phrases are all snippets out of bigger contexts, this example loses its sense with the context. But I totally agree, for learning it is near useless. As I hinted at above "How about" would have made the sense behind it much clearer, if that is indeed what the Turkish part means.
Does it have to mean putting september or october as alternatives like in "how about ..." or could it also mean "how are" as in "I wonder how the weather is in autumn. How are september or october?" (Or would this be "How is september or october?", my english is quite good, but not perfect.)