First of all I want to say you´re really on to something here. I think the app can be of great use for a lot of persons / companies. You´re on the right track to become absolutely fantastic, but you´re not quite there yet!
There are some things that I think you have to better and which in the end will probably decide if the tool is going to be freakin´ awesome or just another nice app...:

1) Branding (I am willing to pay a one-time extra fee for it.)
a) There should be no 24sessions branding. This is confusing to customers.
b) 24sessions sending emails to our customers is a no-go.
c) Custom Domain should not be xxx.24sessions.com, but www.mydomainname.com
d) No "Powered by 24sessions"
e) No 24sessions favicon in the browser

2) Email:
We should be able to control the emails.
a) Do we want to send email > yes / no
b) What should the emails look like > design / text.
c) From email should be our own domain, not 24sessions.com

4) Screen sharing:
The screen shared is shown within the chat window, but the admin / operator can not us the screen. So this is useless. We have to use the actual browser window we shared. That´s ok, but now you can not see the person you chatting with anymore.

5) Points of improvement
a) Rating request after every chat? This should be a setting we can adjust > on, off, chats which took longer than xx min.
c) "1 person" available. This It should say "persons name" is available.
d) "Live now" chat > "Select a date and time that suits you to confirm the booking." > No > this message is unnecessary cause you want to start right away when operator is online.
e) "Live now" chat > why one has to insert name plus email. > just name would do just fine, right?
f) "Live now" chat > button > "Book"? > should be "Start chat"
g) It says; No downloads or installations. But on a mobile device you have to install the 24sessions app...??

I hope you will consider these points and make it freakin´ great!
Thanks,