No to both questions. The only one which might come close is Broken Steel, which expands on the core story a bit. However, it isn't necessary for any core understanding of the main storyline.
The other advantage of Broken Steel is that it does (SPOILER ALERT) allow you to continue playing after the final quest.
According to the Fallout Wiki, knowledge of Fallout 3 is not needed for Fallout: New Vegas, and there are no storyline connections, although like in previous games, there will be the occasional reference to the prior ones in the series.
(I should note that I've not played the original two, and had no issues with 3 and its references to them, so I'm guessing any references from New Vegas to prior ones will be similarly subtle. I do, however, plan on playing the original two!)
Finally, in terms of the DLC, I did purchase, play and enjoy all of them. I was not super-thrilled with Operation: Anchorage, but I thought the others were all exceptionally well-done (even if Mothership Zeta had really nothing to do with the Fallout universe). So naturally your mileage may vary, but it's worth noting that if you want some great additional (and different) stories, the add-ons are, to me, worth the money. Broken Steel is the only one which didn't offer a completely new environment: The others all offered large new lands to explore, with stories to go with them.
Easiest way? Loot the bodies, then drop the loot. This will allow them to despawn/become non-interactive, allowing you to move on to the next corpse.
Best Answer
I have already automated this for you. My solver is available at: http://moria.us/fallout3/terminal.html
Note: this is a single-page application, so you can just save the solver to your hard drive as an HTML file and run it from there.
Tutorial
Let's suppose you find the words RAMBO, DUMBO, MAMBA, BRICK, TANKS. Go ahead and enter those into the solver.
You can see in the right column some of the words are marked as "2 moves" and some of the words are marked as "3 moves". This column is a little tricky to explain, but this shows the maximum number of required moves necessary to solve the puzzle under the following conditions:
You select that word next, and
You play perfectly afterwards.
So you can see that if you select MAMBA, you will need to guess at most two words in order to find the correct word.
Suppose you select MAMBA, and you have 2 positions correct. Click on the
-2-
next to MAMBA:The word must be DUMBO (which is the second move).
During a playthrough of Fallout 3, I noticed that a large number of terminals mostly had "5 move" words with maybe one or two "4 move" words. This means that using the tool, you can play perfectly and beat those terminals every single time... but without the tool, I would abort after three failed guesses.
All you need to do is click a word with a low number of moves.
More information
You can see why MAMBA is the best by clicking on all of the numbers next to MAMBA. No matter what you click, only one other word will be left (or zero).
If you pick a different word, like RAMBO, you might still be left with two choices afterwards. For example, if you choose RAMBO but have 3 positions left, you get:
How it works
"View Source" works fine, it's all JavaScript. If I recall correctly, it recursively calculates the maximum number of moves necessary by examining situations like "what if you choose DUMBO and you have 3 correct". The
maxmoves()
function is where it's at.