Learn Arabic (Modern Standard): الكلب يراني هناك.

When attaching the 'me' pronoun to a verb, Arabic adds a connecting letter ن (n) before the ـي (-ee). This is sometimes called the 'n of protection' because it protects the verb's final sound from changing. Therefore, 'he sees me' is يراني (yaraanee).

The basic form for 'he sees' is يرى with that dotless 'yaa' shape at the end. Why does it change to a straight line (ا) in يراني?

The letter ى (alif maqsura) only takes that curved shape when it is the very last letter of a word. When you attach an object pronoun like ـني (-nee), the ى is no longer at the end, so it changes into a regular, straight alif (ا).

Does the ك at the end of هناك (there) mean 'your' like we learned in the pronoun lesson?

No, in this specific case, the ك is not an attached pronoun. It is simply a permanent part of the spelling of the word هناك (hunaak).

I learned that Arabic sentences usually start with the verb. Why does the subject الكلب (the dog) come before the verb here?

Arabic allows both word orders! While Verb-Subject is the classic structure, Subject-Verb is also perfectly correct and very common in Modern Standard Arabic, often used when you want to establish the topic first.