Learn Arabic (Modern Standard): سيارتي مثل سيارتك.

The word مثل (like/similar to) is a separate independent word, while كـ is a one-letter preposition that attaches directly to the front of a noun. Both mean "like" and are very common in Arabic. You could actually say كسيارتك here instead of مثل سيارتك, and it would mean the exact same thing! This sentence just shows you a common alternative way to express comparison.

The word for "car" is سيارة, ending in a taa marbuta (ة). Why does it look like a regular ت in سيارتي and سيارتك?

When you attach a suffix (like the possessive pronouns ي for "my" or ك for "your") to a word ending in a taa marbuta (ة), the ة "opens up" into a regular ت. This happens because the letter is no longer at the end of the word, and Arabic script requires it to physically connect to the following letter.

How do I know if سيارتك means "your car" addressed to a male or a female?

In written Arabic without vowel marks, it looks exactly the same! If you are speaking to a male, the final letter is pronounced with a short "a" sound (كَ). If speaking to a female, it is pronounced with a short "i" sound (كِ). When reading, you just rely on the context of the conversation to know who is being addressed.

Where is the word for "is" in this sentence?

Arabic doesn't use a word for "is" or "are" in the present tense. You simply put the subject (سيارتي, my car) right next to the information about it (مثل سيارتك, like your car). This structure is called a nominal sentence.