Learn Russian: Почему ты не хочешь хранить печать, которую я тебе подарил? - Why do you not want to keep the seal which I gave you?

Которую relates back to печать, which is a feminine noun. Inside the second part of the sentence (the relative clause), the seal is the direct object because it is the thing that I gave. Therefore, we use the feminine accusative form которую.

Is печать in the nominative case here since it looks exactly like the dictionary form?

It is actually in the accusative case because it is the direct object of хранить (to keep). Печать is an inanimate feminine noun ending in a soft sign. For these specific nouns, the accusative form is identical to the nominative dictionary form.

How can I tell that печать is feminine if it ends in a soft sign?

Nouns ending in a soft sign can be either masculine or feminine, and you usually have to memorize their gender. However, this sentence gives you a grammatical clue: the relative pronoun которую is feminine, which proves that the noun it points back to must also be feminine.

The English translation says 'gave', so why does the Russian sentence use подарил instead of дал?

The verb подарить specifically means 'to give as a gift'. In English, we often just say 'gave' when talking about presents, but Russian prefers подарить to make it clear it was a gift, rather than just an object handed over.