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I would like to know how does the company tiktok make or earn money?

They're not showing any ads, but their users are increasing and their video upload rate is increasing.

Even they have 500 million monthly active users

Also I saw they send t-shirts to more active account owners.

How do they manage the cost of it?

First off you need to consider startups aggressively subsidize their offer early on in order to capture market share. Popular examples of startups valued at billions of $ that were/are in the red include household names like Uber & Spotify that bled money for years on end.
Also, take note social media platforms aim for the network effect and its a crucial aspect of their success or demise (see myspace among a myriad more) so market share becomes all the more crucial in this case.

It is, of course, possible to monetize their user base through ads in the future(as in IG/FB) or enable premium features(as in Spotify/Tinder) but I think this goes beyond just that.

It may sound cliche nowadays but when you don't know what the product is then it most likely is you. Don't forget who owns TikTok, ByteDance which may sound like a random name to a westerner but its a huge Chinese media company with immense success harnessing their user's data through operating several machine learning-enabled content platforms.

It also may be the case they don't intend to make any money off it in the first place, rather use it as a foot on the door to get into the western world where they can leverage their hard-earned expertise globally for bigger and better ventures and what better way to do this by getting into an app primarily aimed to an US-based teenager demographic(one of the best consumer audience group possibly imaginable).

Many companies offer free services to individuals, but charge corporate users for support (example: Red Hat Linux). Could it be that?

Otherwise, it is fairly common practise to offer free services to build a critical amass of users. Once acquired, you can start charging them, although you will probably lose many users. Or, you could introduce premium services, after having let them use the free stuff for long enough to get hooked. Or, even just start advertising.

Another alternative is to grow something so big and attractive that it is bought out by Google, FaceBook, Amazon, Twitter, etc. I remember 20 years ago, when Microsoft paid two college kids over $400 million to buy Hotmail.

In short, we can’t really know what they plan unless they say so publicly. Did you Google? Maybe there is something in the trade press? Failing that, all you can do is wait and see what happens.

[Update] And don't forget - if you are not paying for a service, then you are the product. No doubt they collect - and sell - lots of user data.