Ogromnie proszę o sprawdzenie błędów :)

Hello Anna,

I am writing this letter to you, because I would like to invite you to Poland to holidays. I hope that there will be a fine weather in July and we will be able to much tour. I would like so that you see our most beautiful cities and their treasured monuments. We will tour Gdansk, Warsaw, Wroclaw and Cracow. I would like that you see also saw with Poland nature. We will go to the seaside (Słowiński National Park), lakes (Mazury) and mountains (Tatra mountains - Zakopane). I will try you to get to know the taste of Polish regional dishes. I am asking you to arrive to me for the month of the time. I hope that you will manage to me to arrive and to have a nice time. I am waiting for your response. I am greeting you cordially

to Poland to holidays. -> to Poland on holidays.
there will be a fine weather - > the weather will be fine
will be able to much tour -> will be able to travel a lot
I would like so that you see -> I would like you to see
We will tour -> We will go to/visit
I would like that you see also saw with Poland nature -> I would also like you to see Polish nature
Tatra mountains -> Tatra Mountains
I will try you to get to know the taste of Polish regional dishes. -> You will be able to taste some Polish regional dishes
I am asking you to arrive to me for the month of the time. - Come to me for a month, please. / Will you please come to me for a month?
I hope that you will manage to me to arrive and to have a nice time. -> I hope (that) you will manage to arrive and have a nice time.
I am greeting you cordially -> Greetings from Poland

To list nieformalny, więc możesz używać form ściągniętych, np. "I'm writing..." ;)

Polish nature - tu chyba "the Polish nature"

dziękuję pięknie za pomoc :)

Nie postawiłabym tu "the" - nie jest to aż tak konkretna "nature" (poza tym przed "nature", podobnie jak przed paru innymi - np. "society" w znaczeniu ogólnym - nasze "society" - unika się przedimka. Ale muszę to sprawdzić)

Hello Anna,

I am writing this letter to you because I would like to invite you to Poland {for} holidays. I hope that {the weather in July} will be {} fine, and we will be able to {go sightseeing a lot}. I would like {you to} see our most beautiful cities and their treasured monuments. We will tour Gdansk, Warsaw, Wroclaw and Cracow. I would {also} like {to show you the natural world of Poland}. We will go to the seaside, {to the} Słowiński National Park, {to the lake district}, Mazury, and {to the} mountains, {the} Tatras, with the beautiful city of Zakopane. I will try {} to get {you familiar with} the taste of Polish regional dishes. I am asking you to {come} to me for {a period of one month}. I hope that you will manage to {come} and {that you will} have a nice time. I am waiting for your response.
I am {sending you my warmest greetings}.

Love,
Betty.

engee30, what do you think of "the Polish nature" and "Polish nature"? Which one is appropriate?

And what about that sentence:
"to Poland on holidays." ??
My dictionary says:
- to be/go on holiday - być na wakacjach/wyjeżdżać na wakacje

As for 'for' or 'to' + holidays - I chose 'for' because I like it much better than 'on'. Besides, the preposition 'for' always represents 'the purpose'.

As for 'nature' - you can't say '(the) Polish nature' or what, because the word 'nature' is a general word for 'natura' - and the phrase 'the Polish nature' would be recognised as 'naturą Polaków jest (np. skłonność do kłótni).

Cheers.