Part 2; please read part 1 first.

1/ "Mild" is an adjective; in this case you need a verb. "By moderating our activity, our trip can have a mild impact on the planet."

2/ You aren't talking about a specific list of damages, but damage in general.

Moreover, bad practices, such as overusing cars or overheating houses during winter have a much bigger impact on the environment than one or two long distance flights every year.

When you say "one or two", you need to use a plural.

To conclude, I suggest that the decision about the destination of holidays must depend on different factors other than simply the impact on the nature.

1/ "Of holidays" is redundant here, and makes the sentence sound a little awkward.

2/ The factors are "different to" or "different from", but you would not say "different than". In this case you are talking about factors which are not environmental so I would say factors "other than".

3/ I've added "simply" because based on the earlier part of your essay I don't think you are saying that environmental factors play no part in the decision; just that they are not the only thing to consider.

4/ You don't use "the" because you are talking about nature in general, rather than some specific nature.

Of course the budget is one of these important variables, but it does not affect the final decision as deeply as we could think of a our range of possibile possible choices.

1/ It does not affect... what? You need to specify an "object" that is affected here. In this case, I've added "the final decision" as that.

2/ I'm not sure what the intent of "our" was but I imagine that you are referring to the choices that we have.

Well done.

This has only a few mistakes; otherwise it's well written.

Is it better to have holidays near home rather than travel abroad?

My essay:

Deciding the destination of a holiday is the first difficult step every tourist must take when he/she plans a vacation.

I wouldn't use "of a holiday" there. It's not wrong, but it adds no information since you state that you are talking about planning a vacation at the end of the sentence.

In fact, different factors play a role in it, i.d. the previous travelling experiences, personal tastes and costs.

1/ I think you mean i.e. (id est, or "that is") rather than "i.d." there. I would prefer "e.g." ("for example") however because while this list covers a lot of things, it isn't comprehensive. The amount of time that you can take off from work, for instance, is an issue that you haven't mentioned.

2/ You would not normally use "the" in this case. Again it isn't wrong - it refers to the experiences of the person - but that's implied. Most native speakers would probably drop it.

Quite surprisingly, having holidays near home might be more expensive than travelling abroad. On the one side, in fact, the prices of flights have declined thanks to low cost companies offering long trips for as little as a dinner bill in a medium-range restaurant.

1/ In English it's more common to say "On the one hand" than "on the one side".

2/ "Declined" by itself would be something that happened in the past. "Have declined" means that it happened in the past and is a process that is still going (and having an impact) on today.

3/ With prices it's more common to use "increase" or "decrease" rather than decline. Decline isn't wrong but it's not a common use.

On the other side, the cost of living in places like the Milan area is probably higher than in 70% of the most touristic cities most tourist destinations around the world.

1/ "Touristic" exists as a word but you will rarely if ever hear a native speaker use it. Also "the most touristic cities" would refer to the cities which are highest in their level of appeal to tourists. In this case their comparative level of appeal is less important than the fact that they are "tourist destinations".

Of course, long journeys by plane have a relevant significant impact on the environment.

"Relevant" would raise the question of "relevant to what?" Arguably it could be "relevant to the essay instructions", but I think in this case it would be better to go for something more general. The impact is significant in relation to the overall issue of climate change. Because of Italki's character limits I'll add a second part to this answer.