Exercises in the evening

From a distance, I would hope. The sentence is fine. You should be putting full stops (periods) at the end of them, but aside from that it's fine.

The lion eats the salad

The word "salad" in English is shorter than its Italian version "insalata"

The tv TV show told us that we have no more salad for the rest of the year

1/ Initialisms like TV are always capitalised in English. It's the same as GPS. 2/ If you are quoting exactly what someone has said, then you don't use "that". You generally do if you are paraphrasing. (That is, putting it into other words.) For example, The TV show told us "There will be no salad available for the rest of the year". In this case though, they told you that {some fact or other}. Not all English speakers use it and some would argue that it's optional, but it's probably more common than not.

Many people travel by train to see my lions

Mario got on the train to London yesterday morning

Mario saw a lion while he was travelling on the train

In Italian you don't need an explicit subject; "he was" can be expressed by "era", and you would only say "lui era" if you wanted to be explicit. In English, though, the subject is not contained in the verb. You have to indicate who or what was doing the action. He was, she was, it was, they were, etc.

Mario slept well in the train wagon.

You would normally say "carriage". A train wagon is normally used for transporting goods, a carriage is for transporting people.

The flower shops is on the corner in front of the train station

It has to be either the flower shop is (singular) or the flower shops are (plural).

Inside the flower shop, I see my lion eating tulips in the corner

Thank you in advance for yours suggestions, I know my senteces sentences sound weird but I'm trying to understand English prepositions (and something else).

Good luck. Italian prepositions are a nightmare and I'm afraid that the English ones aren't any better. However your prepositions here are generally correct.