I believe the correction goes more in the lines of subordinate clause (Nebensätze und Hauptsätze) When you use denken (glauben, meinen etc...) you are creating 2 sentences the main sentence "Ich denke" and a subordinative clause "der Kuche ist sehr lecker". You can tell that you have 2 verbs and two sentences hence the comma between them. Commas are very important in german language as they separate the main sentence from the subordinate clause. That's why people correct you the sentence to: Ich denke,(comma) der Kuche ist sehr gut Also that structre is only in spoken language, in text you would have to write: Ich denke, dass der Kuchen sehr gut ist ( I think THAT the cake is very good)

Me : Pronombre primera persona del singular para indicar objeto indirecto ( es decir el receptor de la acción expresada por el verbo es la primera persona del singular - Yo) Te: Pronombre segunda persona del singular para indicar objeto indirecto ( es decer el receptor de la acción expresada por el verbo es la segunda persona del singular - Tu) Tu me compras un Libro ( me es el objeto indirecto de la frase es decir el receptor del Libro soy Yo) Yo te compro un Libro ( te es el objeto indirecto de la frase es decir el receptor del Libro eres Tu)

hubiera sido es una suposicion ( modo subjuntivo ) mientras que estaba o fué son una afirmación ( modo indicativo) Si te ayuda en inglés sería: fué/estaba = It was hubiera sido = It would have been.

Ich bin dreiundzwanzig Jahre alt

I would personally approach a mix, have the tables at hand to know what declension goes with each gender and number, but at the same time try to let the concept for each case sink in you so it becomes natural which case to use. After many times you'll get used to make certain structures and patterns. Once it becomes natural for you use Dativ, Genitiv, Akkusativ and when to use each case, the specific form of the declension is just a matter of a little memory, and a great deal of it will be already covered by the habit of saying certain sentences.

Some people learn faster by doing rather than by studying, I know people who have learned German just speaking with germans, and I know others who like me prefer to grab the raw tools of the language and beat them up until they make sense. It's up to the student to choose what goes better for them time wise and style wise :)