I'd like to see the "free" of 5 with the "day" of 1.

Thank you for remarks.
What do you think about new ones?
Don't search about "concept", but readability, related activity : people from design...
A bientôt !

#2 is the best of the second round — but overall it feels like it's trying too hard to be trendy and 'design' minded. They all look like they're cobbled together from free fonts which makes it look like a knockoff brand.

Hmmmm... Well-well-well... I'm quite agree with you... In a way...
So what is your recommandation? I'm a little lost.
However here is a new one.

If you're lost I'd say go to a sketchbook (or AI file) and just start playing. Don't preoccupy yourself with what you think this has to be. Try to come up with a solid concept behind the logotype (or perhaps mark as well). Look at design blogs, look at other people's portfolios, look at the work of famous design firms and figure out what it is that makes their work successful; do whatever it takes for you to be inspired.

One thing I'm finding I constantly dislike about the logotypes you're showing is that they're all made with a typeface that has something gimmicky about it; something that will most likely date the work within a few months.

From the second round - #3 with 'd' from #2, but I like #3 from the first set the best.