That can be a good solution at least if electricity costs are not a big deal. If power is expensive in your area, it might be worth to buy something more power-efficient, like a raspberry pi (assuming they’re not completely sold out right now).
No company is just going to host a server for you for free, a (virtual) server for running nextcloud will cost you at least a few bucks a month. As others have already said, you can run a server at home on your own hardware, but this is also not free (hardware cost, electricity, etc.) and you will additionally have to deal with any hardware issues & replacements yourself.
That really depends on how exactly the public broadcasting is funded. In Germany for example, this happens independently from other state expenses so there’s no way that the government can directly controll the press. For this reason, the press tends to be critical of all political parties, including the ones currently in government.
From Wikipedia:
Fascism is a far-right, authoritarian, ultranationalist political ideology and movement, characterized by a dictatorial leader, centralized autocracy, militarism, forcible suppression of opposition, belief in a natural social hierarchy, subordination of individual interests for the perceived good of the nation and race, and strong regimentation of society and the economy.
The only part that could vaguely be associated with capitalism (in a democratic country) is “militarism” and even then this is only the case if you mainly focus on the USA. The fact that fascist countries were running free-market economy is also not really a point since that was (and is) the case for a large part of the world.
“subordination of personal interest” and “strong regimentation of […] the economy” is the opposite of prototypical uncontrolled capitalism. Saying that capitalism is fascism is just as stupid as saying that fascism and socialism are the same (“bUT it wAs cALLed naTIOnaL soCiaLIsm”). Using the word “fascism” for everything you don’t like just makes it lose all meaning.
I’m using nebula to remotely access the raspberry pi in my home network and it mostly just works. The dual setup for nextcloud might be a bit more tricky, at least if you want to use HTTPS. You’ll probably have to set up a reverse proxy in Nginx for at least one of the routes, since they need different certificates (although since Nebula already authenticates and encrypts your traffic, HTTPS is probably not necessary there).