I dont know if anyone cares, but i decided to post my progress. Maybe this will be useful for someone in the future. Or not.
So now I have a fully functional system
here is how I did:
I replaced the kernel with a more updated one. I used the kernel from Patwood, 3.4.67 I believe.
Then on boot I insmod module squashfs.ko or else tinycore extensions will not load correctly.
My usb ethernet dongle from china works: just find and insmod modules qf9700 and usbnet.
Usb tethering from an android phone works - insmod modules rndis_host, cdc_ether and usbnet
Wifi has worked! with module 8188eu.
X loads with some errors when unpacking xorg-fbdev, but also works. I am happy because the mini pc seems to get less warm using this system than when I used my debian image, so thank you to the developers. The heating problem is controlled by installing cpufrequtils and underclocking the CPU - I wanted to undervolt too, but I would need to rewrite a kernel it seems, so I am not going to try this so soon.
So, again a big thanks to everyone who has developed this, and have a nice day,