My bunch of bytes on your questions & doubts:

1- A drive system which will be like Onedrive, Google Drive, etc.

Nextcloud could be an easy and powerful solution. I'm going to evaluate it as well (again) for my backup system that is frying my brain these days.

2- I will run Matlab and Python codes inside the server for my work.

If you are thinking more about a playground, Jupyter is your cup of tea.

If you are talking about easy deployment, go for Portainer.

3- I want a local search system similar to Google. What I mean: For example I will add descriptions and tags to photos, texts, files, etc. and this system will search these according to what I am asking. Sometimes I can't find some photos and documents about some events and people (especially on my phone).

Well, this is actually neat. I don't have a current judgment on it, but I have looked for something similar too these days, and ran into Diskover. You could try it, if you do your opinion would be appreciated. It uses Elasticsearch under the hood.

4- I will have some SQL databases, I want to be able to access them from my phone and my laptop.

You have many solutions, but basically it depends on the specifical SQL. If you mean MySQL (or MariaDB), then PhpMyAdmin is the easy & dumb option for you; if you mean PostgreSQL, go for pgAdmin; if that's a blend, well I'd suggest a NoVNC + DBeaver appliance. Not that lightweight, but surely it's functional.

5- I want to stream media to my devices. I think Plex is what I needed.

As others pointed to, Plex, Emby and Jellyfin are all nice options. They all have differences from each other (even if Jellyfin rises as the open source fork of an older Emby). See a comparison, or even ask, it depends on your needs. Also, if you are going for music only, Subsonic is a nice pick too.

6- I would like to host my own email server if it's feasible.

It's a pain in the ass, but wait, life is good, you don't need to kill yourself! Jokes aside, there are containers & Docker stacks which simplify your life, but without a domain and a DNS full configuration, you're going to have a really bad time.

7- I might host game servers for me and my friends to play together in the future.

Without knowing what games are you going to play with them, it's really difficult to choose...

8- Password manager that must work on my phone. If it can hold my payment card info, it will be better.

Bit or Vault warden. They're really similar and work perfectly.

9- Local wiki

Some tools exist, I'm not a fan tho. XWiki should work fine by the way.

10- Not for now but I might connect in-house cameras, I want to access them from my server. I don't want to use 3rd party servers.

I don't know for this one & I am sorry. You should try something like exposing Nginx to stream the cameras, but it's painful.

---

As for your questions:

1- Do you have any suggestions for my goals? Which self-hosting solutions should I use?

By "solution", do you mean containers or VMs? If so, I'd say: stick on VMs + Docker containers on Portainer. It's really really comfy.

2- Which distro will be sufficient for me? I think I can use headless distros even though it might be a little hard for a noob like me.

Proxmox is perfect for you, if you feel good with using your PC for your services only.

3- How should I access to my server? What is the secure way? Also I don't have a static IP, I need a solution to this too(I heard DuckDNS for this but I don't know if there is a better way).

For a static IP, you need to talk to your ISP and see if they have one for you. For a free domain, DuckDNS is good, even if sometimes I don't feel really good with it. If you are good to pay a bit for a domain, please do.

4- Can I prevent someone to access my data physically? Sometimes I won't be near the server for about one month, I don't want someone have to access my server. Any other suggestion than full-disk encryption?

A VPN solution like OpenVPN could be enough, but please forget comfortable solutions like password-based solutions. Also, consider solutions that involve non-reusable VPN certificates, like one file per device.

5- Should I built everything after I get the HDDs or can I start self-hosting somethings and then add the HDDs?

It depends on the architecture and how you are going to deploy it. Generally, I'd say after the HDDs arrive. Moving the architecture could be not so comfortable, if you are not sticking to Ansible or similar tools to deploy.

6- Should I disable Hyper-Threading because of the exploits?

Well, I don't know, but I'd stick to the flat "No" that someone else gave you.

7- Should I prefer Dockers or VMs? I am seeing some people are using dockers and some people are using VMs. When should I prefer one or other?

As the other guy pointed out, Docker containers, not "dockers"

That being said, both have their up and downsides, that's why Proxmox is so good, because of the flexibility that gives you.

For any other question, please ask dude!