Hi, Andrés! Be careful not to say "corrects." I'm sure you know that, in English, we don't have plural forms for adjectives when the noun is plural.
As for your sentences:
1) "I like cooking, not as much as a chef, but enough to stop starving." While both sentences are correct grammatically, we don't say "stop the hunger" when we're talking about our own hunger. Also, notice that I merged the two sentences, because the second sentence is a fragment.
2) "To get a thicker soup, you can add some pasta in." The first sentence isn't correct because "thicken" isn't an adjective; it's a verb that means "to make something thicker." The word "some" is optional in both sentences. Also, there must be a comma between "soup" and "you" because the first part is an introductory clause.
3) "A heatwave is sweltering throughout Europe these days." The verb "swelter" does not take a direct object, so "sweltering Europe" does not make sense.
4) "These high temperatures have been increasing since 2015." The second sentence would be correct if you added "to now" at the end, but because there is no "to (another time period)," we can't use "from" here.
5) "They can see a worsening of their likely fragile health conditions." Notice I added the indefinite article "a" before "worsening." English uses the gerund to describe changing situations.
6) "Avoid exercising outdoors." In Spanish, "ejercicio" is only a noun. In English, "exercise" is a verb as well as a noun, so we only say "do exercise" if we're doing a specific exercise.
7) Both sentences work, but they don't have the same meaning. The first attributes the climate condition to the winds, but the second indicates the winds coming directly from the Sahara are the reason.
I hope this helps. Please let me know if I didn't answer your questions.