Sounds great Edvard
I added some numbers for easier reference:
 Right now, the clock is started and stopped via clicking on the clock text itself; the background changes between light green and pink to indicate the status.
[1a] I'm presuming whichever Task is running is highlighted in some way?)
 The buttons on either side of the clock allow incrementing the seconds/minutes and I planned to add a third for changing the hours, but then I thought about leaving off the buttons, and just set the time manually, or would the buttons still be convenient?
no need for buttons.
[2a] By 'set the time manually', do you mean simply change the numbers in the time field?
 "New Task" sounds good.
[3a] when the "New Task" button is clicked, it stops the clock, enters the Task and Begin time in the next available row. I had planned to make it add the End time and Total time when another Task is entered, but that got me thinking... is that really the best way?
Am I understanding correctly here:
you're talking about starting a new task when one is currently running; and saying that the old one would be stopped and given end-time etc.
So, re [3a] I'm unsure: what would / could be better there?
As it is now, once an entry is listed in the grid, it is not editable, because I assume that the time spent on any task is an important metric, and adjusting for breaks and whatnot should be restricted to within the time spent, not fudging the numbers after the fact; BUT:
[4a] - Should I allow direct editing of the contents after the fact? Of course, one could simply edit the exported text file if the desire arose, I just think it's too much opportunity for 'cheating' to allow in-grid editing, and besides, at that point why have a timer at all? Why not just fill in arbitrary numbers in an Excel spreadsheet?
[4b] - How about deleting rows? (I'm actually OK with that idea).
[4a] is this correct:
the grid will show a start time, and end time, and a total. The total is *not* end-time minus start-time, but will be whatever was shown in the timer clock, based on starting/stopping of same, and including any modifications made by the user.
^IIUC, then, there would be no need to edit anything in the grid. The only thing that might beg editing would be the description i.e. the task name - but if that's in any way difficult, I would leave it out.
[4b] so deleting a row would delete a task?
Could confirmation be requested?
 menus sound good
 eport to CSV would be what I would use