"Tipped back a few" refers to someone drinking. I don't hear this very often. They "tipped back a few beers".

All three can be correct. Between the first and second sentences, I would say the first is better.

They are all the same :)

Basically he is complaining and saying that they are going to send him the leftovers. "I suppose they will be sending me down the odd bits which got trodden on." When he says "the odd bits", that's like saying "the parts no one else wants". "Trodden on", he's saying they've been walked all over. In this case it is probably literal, since he eats grass. But if it's more abstract, it would be like bits that get passed over by other people. Really, the leftovers. Eeyore is saying that they are going to give him what no one else wants. He is being sarcastic about it.

No gain No effort (No pain, no gain)

When he saw coconuts high up in the trees, he wanted to drink coconut water. He thought about how he could drink from them for a while, and thought of the way. (you don't really need to add this, as you mention him thinking about a solution, and then the next sentence is the solution he thought of. So, saying he thought of a solution is a bit redundant.) He thought he should (I might correct it to "He decided he needed to climb a tree") climb a tree, so he practiced climbing a tree for many days. After he learned how, he climbed a tree and drank coconut water. Then, some guys came to the tree and said, "Please give us the coconut water." He thought, I made an effort in order to get them, but they tried to get them without any effort. So he said that, "You guys should practice climbing a tree if you want them. No pain, no gain."

The English is very good! A bit of work on punctuation will really help you refine your writing.

We would probably never say "so I do". I have never heard an example of when you would say that, unless it was in the middle of a sentence. "So do I" is an agreement. Such as, "I really like apples." "So do I!" But "so I do" is not proper grammar unless it might be in the middle of something. For example, if you were saying "I don't like apples, so I do not eat them." But in that case, there is not really anything to compare.

There is not really a significant difference, but you could look at it this way: "Start to do" means that you are not yet prepared to start and "Start doing" means that you have prepared to start. Ex: "I will start to do that tomorrow" vs "I will start doing that tomorrow". The second one sounds more official than the first. As in, if you hear someone say the second one, you feel they really will do what they are saying. Vs the first one, where it does not sound like there is as much conviction behind it. Really though, most native English speakers don't really notice a difference and for all practical purposes, it does not matter which you choose. It is just two ways of saying the same thing, that you intend to do something.

My day in school

Hello! My name is Liza, I am from Russia. And I will tell you about my day in school.
The first lesson is Chemistry. My teacher is a strange, therefore we don't listen her. (what do you mean strange?) Sometimes I try to understand something.
The second lesson is Math (geometry). My teacher is a very very strict, and all of our class is scared of her. I understand a little, but sometimes I understand nothing. But I try, try and try.
The third lesson is PE (physical education). This lesson ("will never be" or "is not") useful. We do nothing.
The fourth and fifth lessons are Physics. Usually we do a lab or we learn a new theme.
The sixth lesson is English. The teacher tell us about something ("the teacher will tell us about something" or "the teacher tells us about something"), and I try to learn and remember that. I like this subject.
After this I go home and do my homework. The day is over.
Thanks for your time!

You are good :) I will tell you, the grammar mistakes are some that I see a lot of people who only speak and write English make too. You are better than some of those people!

Remember to use "a" or "an" before nouns when you are writing. It is the little things like that that you can work on to improve a lot. But you definitely get your meaning across, which is most important :)