I would not use 'possibly' in that sentence. the word "may" implies "possibly". I would say. I may have not turned on the oven. More naturally for me, personally. "I probably did not turn on the oven."

mails

Could anyone help me to revise them? Thank you in advance.

- We are very sorry.  However, due to the production schedule is full, and we cannot  move up advance the time of delivery. The earliest shipment we can make is in the middle of February.  I will make efforts to stay in contact with still try to reach out to the person in charge. If there are any updates, I’ll  I will let you know ASAP.

- Would you please reschedule delivery time for sample A? Try to forward them to the next month. Would it be possible to move them up one month earlier?   Our clients can’t accept the delayed delivery. They are afraid that they will not have the items in time for the season won’t be able to catch the season. Is it possible to get send me back the updated date before noon?

- Attached is a payment list. Please to fill in (note) which on is entries are for sample A and for sample B. 

-The clients complained that our quality is too inferior, and they asked me why we are always late sending  to send the inspection report to them?

It is  almost done!

I will discuss am presenting my final thesis at the university on Tuesday the 11th of July. Finally!!!
I have to admit that i'm kinda I am kind of (OR  ' I am a little') nervous about it!
I know that everything is going to be ok.  I worked really hard to achieve this goal, but I'm feeling a little anxious anyway.  From Tuesday onward everything is going to change, and i'm I am super excited, but I have to stay focused for 2 more days.  After that I will finally be able to concentrate on planning my working holiday experience in Australia.
Can't wait!!

Overall it is very understandable.  However, some very important comments.  'I' is always capitalized.  "kinda" is NOT a veb or a word.  You are writing a lot of run-on sentences.  You need to use periods  I highlighted in yellow where that was occurring.    When we write, we typically omit the contractions, e.g., I'm.  I would write that way iin casual emails/texts to my friends.    

Normally I would say: I took the (or "my") exam last month. The sentence, "My exam was done last month" sounds like you finished the semester, and normally I would say, "My exams were done/finished/over last month" for such an event. If you mean you simply took an exam last month, I would stick with my first sentence, "I took the exam last month." It just sounds better. Both sentences you wrote are fine and have fairly clear meanings, but they do not sound native to me.

My day

I have  had just two double lessons at the lyceum (while this is a word it is not widely used or understood. I would use "high school" or "secondary school") today, but then afterwards I went to the language school. It was an easy day. I also bought a hoody with the picture of lyceum's symbol on it. It is nice and very warm.
Later I visited an event with my sister and her friend. It was an entertaining game which should have taught teach me about working on a team, but it was boring.  All of the exercises were illogical weren't logical.   The leader of this game was inexperienced. My sister didn't like it either too. This game didn't teach us anything.
Now I am a little bit tired. I am going to go to sleep soon.

"If what was said were true" is the beginning of a sentence using the subjunctive where the conditional will follow. The form of the verb (were) is the subjunctive, and many native speakers mess this up all the time. For example, the following is correct grammar: If I were rich, I would travel the world. (What this sentence says is that I am not rich and I am not able to travel the world) If he were more studious, he would get better grades. (He is not studious and does not get good grades.) You can finish the beginning of that phrase you started. "If what was said were true, she would be here by now." (She is not here and what was said was not true.)

Transduction is not correct for changing one language to another. HOWEVER, it is an English word. It means to move genetic material from one micro-organism to another. I know this since I am a molecular biologist. The others probably would not know it unless they are in the field.

FIRST DAY ON ITALKI

Hello there! I know you're not ready for it yet, but here goes a confession: Anxiety's ghost stalks me! And  It's just like having a monster hanging on my shoulder. Sometimes, it really lets me down and prevents me from doings things I like. However this week has been particularly exciting since I've been feeling motivated to take care of myself and achieve some old goals, one of them being improving my English speaking and writing skills and another joining an independent architecture website.

The ghost came out when I was offered a job as an intern at a landscape architecture website, but it didn't turn out well! I just got was terrified about failing at this position.   so I just let it go and allowed my insecurity to beat me once more. I felt truly frustrated and I thought I would never manage to trust myself again.

However, after some reflection, I realized it is not impossible! All I need is to believe in me and respect my own pace. And, More than ever, I'm willing to get it back and, as step in the right direction, I'm joining Italki.  Although I am not the most sociable person ever, I'm a curious girl, and I'm deeply fond of listening to people and learning something new. Besides improving my communication skills, I'm sure I would be able to gain a bit of self-confidence again. So let's get it started!

P.S.: It would help me a lot to get corrections, suggestions for more suitable words, tips on coherence and cohesion etc. Thanks in advance!