The point of the memory test is to ensure it is clean before doing an on-demand scan as there potentially could be something loaded to interfere with the scan. So yes I believe it is important.
No with the memory scan complete yet the Simple User Interface not opening, is a classic sign of remnants of a previous AV. Since we have talked about this in another post, I suggest you get on to this removal of remnants as soon as possible and see if that clears this up.
For one thing, my system is much more powerful than yours, but I wouldn't dream of kicking of an on-demand scan whilst I'm working. I do a regular weekly system maintenance when I also run an avast on-demand scan (Standard sensitivity and without Archives).
Thorough is also by its design very thorough (it scans all files) and perhaps a little overkill for routine use, were a Standard scan without archives should be adequate. Archive (zip, rar, etc.) files are by their nature are inert, you need to extract the files and then you have to run them to be a threat. Long before that happens avast's Standard Shield should have scanned them and before an executable is run that is scanned.
I have only ever done a Through Scan with Archives once shortly after installation just to ensure a clean start state, but with XP for example avast will do a boot-time scan after installation if you select it, this I believe will be quicker and reasonably effective. Like everything in life things are a compromise.
Can you explain exactly what you are doing, because avast is a resident scanner, which starts automatically on boot, you shouldn't have to manually start it unless you are in safe mode (as avast doesn't start in safe mode).
So your comment "Whenever we start avast! anti virus," confuses me a little, why are you doing that ?