In last night I can't slept because of thunders.

Last night I couldn't sleep because of the thunder / last night I slept badly because of the thunder.

You don't need 'in' when you talk about a specific time. You might say 'I often wake up in the night' (general statement) but you also say 'I woke up a lot last night' (no 'in'!). You can also say 'in the morning, I will...' but also 'tomorrow morning, I will...'. Never 'in the tomorrow morning', for example. 

I will marry in next month but I don't choice a bridesmaids yet. But I choiced allready the groom :P

I am getting married next month but I haven't chosen my bridesmaids yet. However, I have already chosen the groom!

'I will marry' is technically correct but very old-fashioned. We usually say 'I am getting married'. Again, you don't need 'in' when you're being specific about the month. Chosen = past participle of choose.

When I cook meat at kitchen my cat is very sneaky and always steel some pice from counter.

When I cook meat in the kitchen, my cat is very sneaky and always steals some pieces from the counter.

In the kitchen not at the kitchen. Steal = the verb to take something without consent, steel = a noun meaning a type of metal. 

Please, don't wear trainers in winter because they are very slippery and you easily can fall.

This sentence is fine!

Great job, well done! :)