Hello and welcome to LQ.
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and modern operation systems are absolutely off limit
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Nope, they are not, only modern Windows versions are off-limit for such a system.
Anyways, building a minimalist Linux from ground up for that system is quite easy if you have the time to learn the basics. In the meantime you might be interested in distributions that are meant for such old systems, like antiX.
To your points:
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- A minimalistic linux with minimal requirements
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Any Linux will do, if you stick to a lightweight desktop environment or just use a simple window manager. Which one of the lightweight solutions you can use depends on how much RAM you have in that machine.
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- Able to play music from USB drive (or HDD ofc)
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Linux has a whole bunch of media players available, from very simple ones to those with media library integration.
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- If possible, flashplayer to connect to youtube lists
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To be honest, while the Flashplayer is available on Linux it is a resource hog and that system may simply be to slow to use it in a reasonable way. Happily solutions like Minitube are available, which will give you access to Youtube without using the Flashplayer, worked for me on a system with even worse specs than yours.
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- Driver for TL-WN322G to connect to network
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From what I read on the Internet this device should work out of the box.
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- Remote control by android phone or another computer (windows based), but that's absolutely optional.
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Never tried it with a phone, but you can use a VNC connection from almost any OS to connect to thjat computer and control it.