No, "у меня" is always related to "me". Literal translation is "by me" but it can have different translations to English depending on the context: "in my..." ("у меня в..."), "at my place." ("у меня."), and sometimes even "I have" ("у меня красивое имя" - ("I have a nice name").

I only spoke Russian as a child so native speakers feel free to correct me or provide a more accurate explanation.

Oh maybe you meant that "у меня" can refers to the luggage therefore it can be translated to "my luggage" as you said? In this case, my answer is still no but the explanation is different: "у мена в..." means "in my...".

If I wanted to say "My luggage is in the room" I would say "Мой багаж в комнате" or "У мена багаж в комнате" which puts more emphasize on this fact being true about me. Like if my parents are mad of my brother for leaving his luggage at the living room and I want to annoy him, I would prefer "У мена багаж в комнате" over "Мой багаж в комнате" which only emphasizes the word "room".

Well maybe you can say "Багаж у меня в комнате" like "Багаж у меня - в комнате" but being written without a dash and with no context of me listing where I tend to put stuff, this is most definitely not the first translation that comes to mind.

Again, I'm not exactly a native speaker so please correct me if I'm wrong.

I understood the same of u

"У + genitive" can carry the meaning of something mentioned or unmentioned that belongs to you. It is often a part of your body, your house, or your belongings.

For example: "Отец у сына." means "The father is at the son's."

So, "У меня в комнате" means "At mine, in the room."

Here меня probably refers to a house or something.

But "У меня в ухе" is literally "At mine, in the ear."

Clearly, at my house in the ear doesn't make sense, меня refers to your body.

No. I don't think you can adequatly translate this sentence into English keeping the Russian structure.

I have the answer to my own question: KOMHATA is the place that the object BAGAZH is being within. The place that the object is being within is subject to the locative case, and the locative case for KOMHATA is KOMHATE.

Here's a list of prepositions, their meanings, and the case of their objects (some prepositions take different cases, depending on various factors, the most important of which is movement): https://forum.duolingo.com/comment/28544274

I guess because that would mean, "My luggage is in the room.", and not, "The luggage is in my room."

No, you have to agree the possessive with the noun in gender, number and case. В моей комнате - there are no other options.

Locative, because the baggage is stationary there. (Locative is formed in the same way as the prepositional case.)

It is not necessarily "with me". It is just in my room (while I may be anywhere else).

See JewishPolyglot's comment above.

Not a native speaker, but I think you have to keep "у меня в комнате" together.

A language can have more than one way to say something; see olimo's comments above.

"в моей" because is has to be preposition case.