She asked me how my day was and anyif anything had changesd for me recently.

This can also be "if there were any changes for me recently".

I told her that I didn’wasn't getting along well with my roommate and that we often quarreled.

I'm not sure if your disagreements with your roommate are only something that happened in the past (in which case, you were right), or if this was something that was still happening (in which case, my correction would be more appropriate).

I think the key problem is that we didn’on't know each other well.

Make sure that your tenses agree with each other. Once again, I don't know if these events are still taking place (you would use the words "is" and "don't") or if they are just something of the past (you would use "were" and "didn't").

There have been many misunderstandings since we first met, so theywhich have affected our relationship.

From her behavior, I know exactlyfor sure that she dislikes me.

I came up with a method for saving money method and it is sovery easy.

There is nothing grammatically wrong with this sentence, but it is a little awkward.

What do you think? She didn’t say a word, and with an impatient expression on hiser face, and tshen left our apartment.

Make sure that your pronouns agree with each other. When referring to women/girls, use "she" and "her". In reference to boys/men, say "he" and "him".

My friend comforted me and said that it was alright, s. Sometimes, no matter ifwhether or not you are kind or not, there is someone who dislikes you.

In English, we call this a "run-on sentence". You can usually fix this issue by starting a new sentence instead of just attaching a new idea with a comma.