Learn Hardcore German: Ich trage meine Sonnenbrille im Park.

Sonnenbrille is a feminine noun (die Sonnenbrille). When it’s the direct object of tragen, it takes the accusative case. In German, possessive pronouns before feminine accusative nouns get an -e ending, so mein → meine.

Why is im used instead of in dem in im Park?

im is simply the contraction of in dem. Since in plus the dative case indicates location (“where?”) and der Park (masculine) becomes dem Park in dative, you get in dem Park → im Park.

Why is the dative case used in im Park and not the accusative?

German prepositions like in govern different cases depending on meaning.

Dative with in = static location (“in the park”).
Accusative with in = direction or movement into (“into the park”).
Here you’re saying where you wear your sunglasses, not where you’re going, so you use dative.

Can tragen mean both “to wear” and “to carry”?

Yes. Context decides the meaning:

With clothing or accessories, tragen generally means “to wear.” (“Ich trage meine Sonnenbrille.” = I’m wearing my sunglasses.)
With other objects, it can mean “to carry.” (“Ich trage die Tasche.” = I carry the bag.)

Why doesn’t German use a continuous tense like “I am wearing”?

German doesn’t have a separate progressive aspect. The simple present tense covers both habitual and ongoing actions. So ich trage can be “I wear” or “I am wearing.” If you want to stress the “right now” aspect, you can add gerade:
“Ich trage gerade meine Sonnenbrille im Park.”

Can I change the word order and start with Im Park?

Yes. German is a verb-second (V2) language, so you can front an adverbial for emphasis:
“Im Park trage ich meine Sonnenbrille.”
The finite verb trage remains in the second position.

Why do we use the singular Sonnenbrille when English says “sunglasses” (plural)?

In German, a pair of sunglasses is considered one item: die Sonnenbrille. You only use the plural Sonnenbrillen if you mean multiple separate pairs.

What’s the difference between tragen and anhaben when talking about wearing something?

tragen = general verb “to wear” (or “to carry”). It takes a direct object: Ich trage mein Hemd.
anhaben = separable verb meaning “to have on” (colloquial). It doesn’t take a direct object but uses an: Ich habe mein Hemd an.
Both can describe clothing or accessories, but anhaben can’t mean “to carry.”