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The first thing I think you need to think about is that the logos are fairly difficult to distinguish. I thought it said Avitart until I read your description, and the top ones almost look like Asia.
webdesign really runs together and should probably have some sort of division.
I think 2a is my favorite of all, but concept 1 really intrigues me.
I'm curious as to what the mark is supposed to represent? Do the green dots mean anything? Is there a reason they are in the place they are? Is the mark supposed to look like a lowercase a? If so I have to wonder why as it doesn't seem to really fit your name.
As was said earlier, the fonts are a little bit weak, especially in concept 2 and "webdesign" in 1a.

Patrick, dots do not mean anything....they are just part of my style which I tried to reflect in the logo. The same with the mark. Your questions are very valid to ask when designing a logo for a client. But here I do my own personal logo. Everything I want it to do is to reflect my preferred style of design or my personality. Thank you for the feedback.