When I reply to an email, it is automatically marked as read. I want to mark it manually after I make sure there are no more actions required for this particular email. (Sometimes I want to answer one issue from an email and leave some more for answering.)
Unfortunately, Outlook 2010 does not seem to have that feature. Replying to a message marks it as read.
Though, if I may suggest an alternate approach to your problem: Consider the solution of having anything in your inbox being "unprocessed", and then using folders for what you have dealt with. Completed emails shouldn't be in your inbox view anyway. You are clearly a power-user of email, perhaps you could even get some peace of mind by not relying on Outlook marking emails bold and not?
To address your other concern: If you are in your inbox and hit the "From" button, you get a straightforward grouping of emails. That way you could easily go through "all the work that needs to be done for a given customer". You could also search, but only in your inbox, for the same effect.
I don't think keeping emails unread is the way to go. You actually read the email so it should stay that way as read so you know what's new and what's not. If you want to keep track that you still have to do some work for the client or so then use Flags or colors.
If the email is something I have to remember to do I always mark it with a flag and then it pops up on my TODO list. It's clearly visible there. I also recommend using colors for grouping particular emails if necessary.
And when you're done with it you mark it as done:
Keep in mind thou that marking it as done may not work on all types of accounts. It works on Exchange and POP3 but doesn't work on IMAP. The flag simply disappears on IMAP account
Remark: A quick shortcut to mark an email as unread is Ctrl + U. Mark as read is Ctrl + Q.
A workaround for your problem might be to adjust the Outlook 2010 timer for marking items as read :
Go to File tab => Options => Mail => Reading Pane. Check the box for
Mark items as read when viewed in the Reading Pane, then Enter the
Number of Seconds you would like Outlook 2010 to wait before marking your email as read.
This setting adds a delay to how long it takes to mark your messages as read. Once you have it set, Outlook will wait for the allotted amount of time before automatically marking the email as read. Switching to another email before this time is up will terminate the timer, so the email will never be marked as read.
Setting this delay to very long may in effect disable the automatic marking as read.