Being in a new place gives me a lot of strange feelings.

My first day isiswas 
Since you are talking about your first day that has already happened, you need to talk about it in the past tense. Thus, 'my first day WAS'.

full of feelings: happiness , anxiety, scared fear and stressful. 
Feelings are nouns. The nouns associated with the verbs of feeling you described are as listed.

I decided to control my feelings in this case to do good in on the first day,  Alsoand to get a good first impression about of the university.
The proper prepositional phrases of the events you are describing are "on the first day" and "first impression of". You basically have to just memorize these (there aren't really any grammatical explanations behind why the prepositions are used the way they are like this). These two sentences would also flow better if you made them into one. Thus, I added a comma after 'day', added an 'and' in place of 'Also". Since you are discussing something that you DID to achieve particular outcome, that outcome would stay in the present tense. You did a good job of this in saying "to do good on the first day", so you also have to keep the tense in the present form and say "to get a good first impression". 

Making a list of my day jobs daily tasks is also a way to gain a good start in the new place.
"Making a list" is the correct way to describe an action that you do in general, since that is the tone that this sentence gives off. I'm not sure what you mean by 'day jobs', but at least here in America, a day job is something you do from 9 am to 5pm at night. You seem to be talking about tasks to do throughout the day, so I wrote "daily tasks" for you.

I hope these explanations are helpful! Let me know if you have any other questions (: