From your last few screen shots, you are in your installed OS (prompt) not the liveOS.
You can boot into the installed OS now.
The errors show xorg/xserver issues.
However, I am not good in these things (xorg/xserver) and if someone else can help, that will be best.
To fix it, again go into prompt (use '3' at linux line - hope you know this time) and use the commands the people here give you.
If you can tell them what your graphic card is, and whether any dual graphic cards, it will be good.
The best info would be
ps: my (unexpert) advice (only in the case of non-dual or fancy graphic cards)
if nvidia use non-free; if amd, use free
to fix , I (nonexpert) do this
remove all drivers in 'mhwd -li'
sudo pacman -Syyuu
install the appropriate driver (just one)
do again 'pacman -Syu' (to fix missing xorg/xserver, if required)