Vikunja is the only viable thing. CalDAV spec allows to assign tasks, but we got XMPP moment here - spec exists, but almost no apps implement it properly.
Also you may take a look at https://github.com/awesome-selfhosted/awesome-selfhosted#task-management--to-do-lists
Take a look at HDMI versions in wikipedia and select cable accordingly.
Don't go with "cheapest" advices as you might buy cable that only capable to FullHD@30Hz, which I think not what you want.
Also, if your card and TV have displayport I'll suggest to go with that instead of HDMI. It just better and does not forbid open source realisations, like HDMI consortium does on HDMI 2.1.
Syncthing is a sync utility wich is different from a cloud service. They both have different purpose and are for different tasks.
They all do one thing - syncing files. And less painful implementation done by nextcloud, at least for me.
Using Caddy for couple of years already at home, yet using certbot at job, because of requirements to use nginx as balancer.
I'm using nextcloud for files and photos/videos sync from mobile, Joplin for notes and tasks, baikal for calendar (with sharing with my wife which using iOS/macOS).
There is nothing better than Nextcloud for files, I was trying to use syncthing and seafile - both sucks in one way or another.
Also, I was using vikunja for tasks but it's UI and UX... Well, strange and not eye-candy. I hope someday they'll rewrite it.
They're in wiki markup by default. Markdown is a separate plugin IIRC.
It virtualises only parts of operating system (namely processes and network namespaces with ability to passthru devices and mount points). It is still using host kernel, for example.