The hard drive of my laptop is absolutely off. I use plop boot manager and boot a live usb flash drive. How can I use it to save updates, settings etc? Should I make two partitions, one for boot and one for saving? Or I can save to the booting partition?

Make it a Persistent Live USB , this video help me.

Thank you. But while waiting for answer, I used the"install" icon on the live Desktop to install the system to a 16GB usb flash drive. I test it now and it's very slow. It' s because the installation method? The format is ext4, this was the recommended one.

Antix2usb doesn't seem to work at live session. It asks for the password, I write"root" and then nothing seems to happen.

USB1 and USB2 are slow. USB 3, I can live with.
Try demo

OK, I made it with antiX2usb, I formatted it ext2 and it's quite faster. I wonder if fat32 would be even more.

fat32 is much slower

For me persistent Live USB was much faster than installation to usb.

Persistent live is faster, indeed.

ext2 is faster than ext3 & ext4?

Should I upgrade the system?

Try persistent Live USB , bet you like it. I use ext4.

Yes, persistent Live USB seems to be OK. It also seems that the 16gb flash was not so good, so I used one 8gb and it's faster. Ext4 is fine. I decided to make it dual boot. I created a partition about 5.5gb and a second one about 2gb. I used antiX2usb to put antiX into the first one. I gave 1gb to root and 3gb to home. It seems to be OK. Then I used Unetbootin to put TahrPup 6.0.5 to the other partition. This is something slow. I think to give it more space, but what to reduce at the first partition?

And something else. I have to use every time gparted to move the boot flag from one to the other partition. Is there a way to install grub to flash? Thanks

For ease of use, I generally use 1 stick for each distro.
Saves wiping drives in the long run.

Take gparted to the 16 GB stick, I have found several bunches of different partitions on them. Getting rid of all the extras sure made a difference.

I tried to wipe the 16gb flash, I don't know if I did it well, there was an error.
Then I formatted it ext4 with gparted and put antiX to it with antiX2usb. The help video says that if you enable root persistence you don't have to enable home persistence, but any time I enabled only root persistence I had problems, so I gave 4gb to each of them. After all, it's still slow. The other flash, this with 8gb (and only 5.5 of them at the partition) is faster. I think that cpu works better with this. It's always around 100%. With the 16gb flash, the percentage is most time much lower.

For Gparted
I insert the USB stick
then Menu> Applications > System tools > Gparted
Use the drop down top right to select the Stick
Now look at the graphic closely.

That was how I found the garbage on it and removed all the partitions as I could then see them and remove each one in turn.

But that's what I've done. I deleted all partitions and I make a new one for all device, formatted ext4. But this didn't make the 16gb flash drive fast enough. I think it doesn't make good use of CPU, because of the low percentage I see most time.