Temperature/Weather Lamp
I want my lamp to turn colors after the temperature outside and maybe add some weather features.

Moon Lamp
I want the lamp to be in sync with the moon’s cycle. When the moon is full, the whole lamp glows, when the moon is half, the lamp lights half. I want that to be a wall lamp so it’s more clearer.

JellyFish Lamp
This lamp has small motors that makes the jellyfish look like it’s floating in the air. I got the inspiration from the link below:

Great brainstorm, Gudrun! Feedback below.
1. Temperature/Weather Lamp
This has been done many times, so if you pursue this idea you’ll have to be able to differentiate yours from the rest. https://ifttt.com/ has a weather applet, but i don’t think it’s hourly temperature. you could also connect it to an outside thermometer using wires or the internet.
temperature sensor https://www.adafruit.com/product/4369
Here’s a project I did using IFTTT’s weather service a while back https://beckystern.com/2017/02/21/modern-wifi-weather-display-with-arduino-esp8266/
2. Moon Lamp
With your mechatronics background, I encourage you to take on something with movement, such as this or your third idea. You could have a motor at the top that spins an opaque sheet, occluding part or all of the moon face. It might have to be a sphere instead of a half-sphere, so the pieces inside can rotate without having to become flat at any point.
3. JellyFish Lamp
Since this is already a product, i’d want you to differentiate yours. But the upside is that there are lots of 3d files available, and you could upgrade/change them to make an elegant, reproducible DIY edition.
https://www.tiktok.com/@printedloots/video/7199378779909770542
https://www.printables.com/model/285573-jellyfish-swimming-mechanical-interactive-art
general resources for you: https://learn.adafruit.com/adafruit-motor-selection-guide?view=all
i think you probably want to use a servo motor (pay attention to standard vs continuous rotation), but a stepper would be quieter and more of a challenge.
there are a bunch of easy-to-use motor drivers on adafruit: https://www.adafruit.com/search?q=motor+driver