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.
Best Answer
The towers are there to provide atmosphere, but they don't advance the plot or otherwise "do" anything. In other words, they're part of the backdrop meant to make the world feel authentic.
Powering up a tower will make it start transmitting a signal, which in most cases is a repeating Morse code message. You can use your PipBoy to locate the source of the transmission, usually a ham radio in an underground bunker near the tower, accessible through a drain. Some of the bunkers have decent loot.
Most towers transmit a very simple Morse code messages that basically say "Hello, is anyone out there? This is [station ID]. Please respond." But two of the towers instead transmit audio recordings, one of just the sound of breathing.
This Fallout Wiki page lists all the broadcast towers, explains the Morse code signals, and provides links to each tower where you can see its specific message.