Welcome to Android Forums, Broca89!
1) how can I automatically save the photos I receive on my phone
By using any of numerous apps/services. The easiest and most obvious, since it's the de facto standard on Android, is
Google Photos. Once set up, it will save your photos automatically if you choose. But there are many other options, including Amazon Photos--which includes unlimited storage for Prime members. Or you can use cloud storage services, such as Google Drive, Amazon Drive, Dropbox, etc.
together with all the photos I have in my gallery?
Your 'gallery' is simply an app that displays your images. The images themselves reside in various directories on your device. If you choose any of the options mentioned above, you'll be able to choose which locations automatically get backed up.
And how can I move those photos manually?
With a file manager, or good gallery app. My favorite file manager is
MiXplorer Silver; its capabilities include connecting to various cloud services, and also local networks. I rely on both of those features daily. My favorite gallery app is
F-Stop Gallery Pro, which also connects to various things and allows file management, like moving or renaming images.
2) why do I not get a preview when I receive a Whatsapp message? I can’t even see who sends the message.
Go into your System Settings, find WhatsApp in your apps list, then go to its notifications. You can adjust your alert preferences there.
If you're not sure how to do something, just ask!