1. trotz + which case?
The word trotz is a preposition. It can be used with genitive case (which is the standard usage) and in rare cases also with dative case. In Swiss German the use with dative case is more common than in Austrian German or German German.
You just have to learn which preposition wants which case. There are lists of prepositions in German books (and also online) that can help you with other prepositions.
Standard usage für »trotz« is genitive case:
Es war trotz des Regens angenehm warm.
But in some cases dative case is used:
Eine Woche nachdem Walters Frau ihn aus der Wohnung geworfen hat, verlor er auch noch seinen Job. Trotz allem gab er nicht auf.
And, as said above, in Swiss Standard German (I'm not talking about Swiss dialects!) you also can use dative case where you have to use genitive case in the two other standard variations of german:
Es war trotz dem Regen angenehm warm.
Note, that the word »trotzdem« ("nevertheless") results from this dative usage: trotz + dem
2. all(e) meine(r) Zimmerpflanzen
The subject of your sentence are all of your room plants. For a moment we can forget your efforts, and try to build a very simple sentence with your subject:
Die Zimmerpflanzen sind gestorben.
The room plants died.
Now you can add the information, that this was your plants:
Meine Zimmerpflanzen sind gestorben.
My room plants died.
This should be clear so far. But what if you want to tell, that all room plants died? You can replace the personal pronoun »meine« by the indefinite pronoun »alle«:
Alle Zimmerpflanzen sind gestorben.
All room plants died.
But now the information, that it was yours is missing. But you can say both. In English you can say it in two different ways:
- All my room plants died.
- All of my room plants died.
In English, as far as I know, the second version (»all of my ...«) is more common than the first one.
Both sentences say the same thing, but in different ways. In the first sentence you just say, that all your plants died. In the second sentence you say, that there are room plants that belong to you, and from this set of plants all died. The difference between both sentences is, that in #2 you talk about a subset (that contains 100% of the full set) that died, while in #1 you directly talk only about the full set. This is a very tenuous and very academic difference, that most people will not notice when they hear one of this sentences, because both sentences at the end of the day exactly mean the same: All plants are dead now, and it was all plants you owned.
You can make this difference in German too if you want:
- Alle meine Zimmerpflanzen sind gestorben.
- Alle meiner Zimmerpflanzen sind gestorben.
Both sentences are absolutely perfect and 100% correct German. But in German the version #1 is more common.
But from the common #1 there is also a variation which is even more common:
- All meine Zimmerpflanzen sind gestorben.
There is an interesting fact about the indefinite pronoun all: If the indefinite pronoun »all« is followed by another pronoun, then the grammatical personal ending of »all« (the »e« at the end of »alle«) can be omitted. (Technically it moves to the next pronoun, but since this other pronoun already always has such an ending, it can't be used there and therefore vanishes.)
So, here are the three versions of your sentence, that are correct and mean the same thing:
Trotz meiner Bemühungen sind alle meiner Zimmerpflanzen gestorben.
Trotz meiner Bemühungen sind alle meine Zimmerpflanzen gestorben.
Trotz meiner Bemühungen sind all meine Zimmerpflanzen gestorben.