If you followed the instructions you have linked to, you probably have installed lightdm which is not only unneeded but probably the cause of the error messages you described.
I suggest to start from scratch with a fresh Volumio install. Then try the following steps:
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Install the Touch Display plugin.
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Download the display specific overlay:
wget https://github.com/goodtft/LCD-show/raw/master/usr/tft35a-overlay.dtb
Be aware that I can only guess what overlay could be needed as long as I don’t have more information on your display. 
- Copy the overlay to “/boot/overlays/tft35a.dtbo”:
sudo cp tft35a.dtb /boot/overlays/tft35a.dtbo
- Open “boot/userconfig.txt”:
nano /boot/userconfig.txt
- Add the following lines:
dtparam=spi=on
dtoverlay=tft35a
It could be necessary to add a rotation value to the overlay later on.
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Save “/boot/userconfig.txt” by typing Ctrl+x then y and Enter.
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Download “99-calibration.conf-35-0” as it might be necessary to calibrate the screen:
wget https://raw.githubusercontent.com/goodtft/LCD-show/master/usr/99-calibration.conf-35-0
Again the data in these kind of files depends on the particular screen and without having more details of your display the values might fit your screen… or not
- Copy “99-calibration.conf-35-0” to “/etc/X11/xorg.conf.d/99-calibration.conf”:
sudo cp 99-calibration.conf-35-0 /etc/X11/xorg.conf.d/99-calibration.conf
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Reboot.
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If the display should not have the orientation you are looking for, add a rotation parameter to the overlay in “/boot/userconfig.txt” so it looks something like this:
dtoverlay=tft35a:rotate=90
This would rotate the display (not touch) by 90 degrees clockwise.
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Reboot once again.
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If the display rotation appears to be correct now, check if the touch function is already properly aligned to the display. If this should not the be case try to find out by what amount touch has to be rotated. Then head over to the Touch Display’s configuration page and set this value in the rotation setting.
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Reboot and check if touch is properly aligned to the display now. It is possible that setting the rotation in the prior step does not suffice. This would be the case if the touch axes are inverted or swapped which is not uncommon on these kind of screens… Then you would have to find out how the axes inverted or swapped. Report back with your findings so we could try to find the right values to correct that.