Here are the solutions for each sentence, explained:
1. **Axel does not play chess every day; he prefers backgammon or billiards.**
* **Explanation:** The sentence describes a regular habit or preference. Since Axel doesn't play chess every day, we use the Present Simple negative form. The verb "not to play" becomes "does not play".
2. **I am not playing marbles; I'm just watching my friends play.**
* **Explanation:** The sentence describes what is happening at the moment of speaking (or writing). The speaker is watching, not playing right now. Therefore, we use the Present Continuous negative form. The verb "not to play" becomes "am not playing".
3. **Marina is writing amazing poems, she's a good poet.**
* **Explanation:** This sentence describes an activity that is ongoing around the present time. Marina is writing poems, suggesting that she is currently in the process of doing so. We use the Present Continuous form of "to write", which is "is writing".
4. **Wait! I am writing a message to my mum right now.**
* **Explanation:** The word "Wait!" and the phrase "right now" indicate that the action is happening at the moment of speaking. Therefore, the Present Continuous tense is appropriate. The verb "to write" becomes "am writing".
**In summary:**
* The Present Simple is used for habits, routines, general truths, and facts.
* The Present Continuous is used for actions happening at the moment of speaking, or for temporary actions happening around the present time.