All these sentences are correct except "this lesson is so annoyed/bored/confused". These sentences are incorrect because you are associating a very "human" or at least "sentient" attribute towards something which is not alive. When you say "this lesson is so annoyed", it implies that the lesson in question is a living thing, capable of having an emotional reaction. It does NOT mean that some other individual finds the lesson boring. "I find that lesson boring." would associate the "feeling" with an individual, regarding an inanimate entity. Likewise, the pronoun is not necessary here. One can also say "The lesson is boring", it would also imply that someone else finds the lesson boring. Similary, one can say "I am bored", implying that an individual is feeling bored due to some undisclosed reason, but "The lesson is bored", would be incorrect, since the lesson is not an entity and cannot have an emotional reaction by itself. One can have an emotional reaction about it, but it cannot have an emotional reaction about anything else.

"Hang in there" can be a more "comforting" statement, for someone who is hurting or in pain, and you're asking them to be a little bit more patient with their circumstances, or just to offer them kind words of encouragement. Something similar could be "there there". It's a gentle phrase, with a rather passive tone. Where as "fight it" sounds much more active and almost militant. "Fight it" would literally be a war cry of sorts, to encourage an individual to keep resisting/fighting some form of hurdle. Though both can be used in situations of distress, but one has to be careful. For an individual who is in a state of mourning "hang in there" might be gentler. For someone who just needs a bit of encouragement to get up, "Fight it" might be better.

Might I suggest that you write the press release and afterwards upload it. I am sure there will be loads of people who would love to edit it for you.

I am really sorry for your loss. I have made some edits to your text, hope this helps :)

My friend, who is standing the middle amongst us, passed away four days ago. Unfortunately I was not able to visit his home to pay my respects and offer my condolences to his family, and that makes me very sad.

you can either use "pay my respects" or "offer my condolences".

My sport activity

When I was a child, my father teached (taught: past tense) me (how) to play football. From (with time we use "Since", "Since that time") that time I couldn’t live without regular exercises.
("During different times" or "In different phases") In different times of my life I (have) preferred different kind(s) of sport activity.

I often played football when I go (went: past tense) to school and (also when I) studied at University. Then I began to do ("practice" sounds better) Kung-Fu exercses ("excercises" is not needed) two times ("twice" sounds better) a week. At the same time I (also) went to a swimming pool.

I like to go out (of the) a city for the weekend so (that) I (can) ski in (the) winter. Fortunately my wife likes sport too. We always do exercises together and I’m very happy about it.

_____

"I like to go out of the city for the weekend, especially during the winters so that I can ski." < this would be better!