「わたしの」は必要ではないけれど、間違ってはいません。当たり前とはいえ、「わたしの」は話し手の強調でしょう。

私の友だちの家には可愛い犬が三匹います。

ともだち、友だち、友達

は is the particle that is used to indicate the the subject, object, complement, adverbial, etc. "わたしの友だちのいえに" (in my friend's house) is the adverbial of place here. Some examples: 桜の花は美しい。(for subject) この映画は先周见ました。(for object) 教室へは行きません。(for adverbial of place)

Using には instead of just に is putting emphasis on the location, or contrasting it with some other location but since there's no context we don't really know.

Both に and には are correct here.

"In my friend's house," vs "My friend's house"

This is called phonological assimilation - a consonant becomes more like the previous one. In this case, "h" assimilates to sound more like "n" that precedes it.

It's very common in Japanese when "n" and an unvoiced consonant meet (usually "h" or "k"). H- syllables then become their voiced variants, b- / p-. Similarly "k" becomes "g". Contraction and assimilation of いち and ろく when combined with counting words is also common.

Some examples: さん+ひき --> さんびき (three small animals)

いち+ひき --> いっぴき (one small animal)

さん+かい --> さんがい (third floor) BUT さん+かい --> さんかい (three times)

さん+ほん --> さんぼん (three long cylindrical things)

If you don't know the correct variant from memory, it's safe to assume that if there's いち or さん before the counting word, and the counting word starts with unvoiced consonant, it will assimilate.

さんびき => sampiki => sambiki

(like greek μπ)

I think it would need to be 三びきのかわいいいぬ So there would have to be a の between the counter and the noun when the counter word isnt at the end of the sentence

They want the number right before the verb