I like to describe there why we have choosed current design. Please let me know if the current design or suggested by trackman seems better for you.
I am refer the original .doc file sectons later.
1) We have placed "Hello" and search bar below menu because menu contains many elements, graphics and catch attention. It's more natural for human to scan page down later (because we read top-down), not up. I am worry, that search bar will be in the blind area otherwise.
2) Many new users have problems even with task creation/filtering in TS 3.5. Our goal in 4.0 was to create very visible buttons like "Submit a bug" or "My issues" on a toolbar. Because we cannot place all task categories and all filters to the toolbar, we move rarely used to menu (we have taken this idea from gmail UI). So I like to left most popular user actions on the toolbar, not hide them in menus.
Another our goal - avoid "task", "filter", "message" wording on user pages, I think this is extra concept and more direct wording should be used. For example, instead of "Task Actions"->"Note" I prefer "Add a note" or "Comment this issue".
In TrackStudio 3.1 we have menu item "Create a task" and many customer ask us, how to create a project. In 3.5 we have changed this to "Create a task or a project" and customers ask us often "What is the difference between task and project". I like to solve this problem forever

Our main goal there not to reduce mouse clicks or improve navigation, but to make UI more task-driven: user likes to "submit issue", not "create a task".
3) We have decided to remove "task description" wording and frames around description to make it more similar to plain document. Task should looks like plain document (title, body, etc), all task fields like submit date or assignee should be somewhere else.
Some issues trackers (JIRA) move this info to the left part of screen, but we already have tree there and this is not possible in TS, so we have moved it below.
4) You suggestions looks fine, I'll discuss it with developers.
5) In TS4 you can mark a few message, click "Note" and selected messages will be quoted. This is my reason why we require buttons around message list, not just the last message.
If you use ASC sorting order for messages, TrackStudio will place last message to the bottom of the page. In this case, you can open task page, read name and description at the top, click "->" button and move to the bottom of the page with last message and list of actions. You needn't to scroll down/up the page to search the "Last message" area .