Learn German: Ich habe mein Portemonnaie in der Tasche.

The preposition in is a two-way preposition. Because the wallet is already resting in the bag and not moving to a new location (answering the question Wo? or where), it takes the dative case (der Tasche). If you were actively putting the wallet into the bag, you would use the accusative (in die Tasche).

Why does the German sentence use der Tasche (the bag) when the English translation says "my bag"?

In German, it is very common to use the definite article instead of a possessive word (like meiner) for personal items, clothing, or body parts when the owner is already obvious from the sentence. Saying in meiner Tasche is grammatically fine, but in der Tasche sounds much more natural here.

Could Tasche also mean "pocket" in this context?

Absolutely! Die Tasche can mean bag, purse, or pocket (often short for Hosentasche or trouser pocket). Without more context, this sentence could just as easily mean that you have your wallet in your pocket.

What gender is the loanword Portemonnaie and why is it mein?

It is neuter (das Portemonnaie). Because it is the direct object of the verb haben, it is in the accusative case. For neuter nouns in the accusative, the word for "my" is simply mein with no extra endings added.