One thing I have always liked about this forum, is there are people willing to help others. With that said, there are a few things in this thread that need to be corrected.
"And with a directional antenna, you'd basically have to have that signal pointed directly at the antenna for it to make a difference." "Even with a high-gain omni-directional antenna, you won't have to worry about much interference across only 80 meters."
Both of those statement are incorrect. Without doing a survey to see what other modulated or unmodulated signals are in the area, you could have issues. It has also been proposed you use TL-ANT2409B antenna which as a horizontal beamwidth of 60°. The TP-LINK TL-ANT2412D has a horizontal beamwidth of 360°. You are going to be throwing signal all over the place. As soon as you run into any co-channel interference from other wireless networks, they are all going to be contending for time to talk within the same channel.
As for the friends that live below you the TL-ANT2412D ony has a vertical beamwidth of 12°. The worst place for clients to be around an omni direction antenna is above or below the antenna itself. The signal dispersion of an omni directional antenna that has around 2 dBi of gain looks like a doughnut. As you increase the gain on the omni, the signal dispersion will start to look more like a pancake.
Omni Antenna Pros and Cons
"The advantage of having two antenna is to reduce dead spots near the access point." Diversity does not work to fix dead spots near the access point. Diversity is used to solve multipath issues, and signals being out of phase. http://www.cisco.com/en/US/tech/tk722/tk809/technologies_tech_note09186a008019f646.shtml
One thing I did not see in this thread is how the rest of your network is setup. For the connection from window to window across the 80m, this needs to be on a different channel and SSID from the access point you are using for your personal use inside your house. I can only assume you already have an access point for your personal wireless devices. If there are any other users in either building using the same channel you are using for the link between the buildings, you are going to have issues. You are going to end up with a Near-Far problem and a Hidden Node problem. This is going to cause collisions, and a ton of retries. If you are on the same channel for your personal wireless, they will carry over and cause your laptop to have issues.
Hidden Node: https://www.youtube.com/watch?v=WjZ8wi5Qggc
You said you live in a building, and I bet there are a bunch of wireless routers there.
The only way i see this working with 2.4 GHz is using two Parabolic Dish desktop antennas (if they make them), or possibly two Yagi antennas. You can see the beamwidth and signal maps on this page. http://www.cisco.com/en/US/prod/collateral/wireless/ps7183/ps469/product_data_sheet09186a008008883b.html
Look for AIR-ANT3338 and AIR-ANT1949. I am not saying buy these as they will be expensive. I only deal with enterprise grade wireless, so these are only examples to show you.
If it were me, the only way I would attempt this project would be to use 5 GHz. There are a bunch more channels you can use to get away from other modulated signals. There are also only a few unmodulated signals that would cause you interference such as doppler radar. With using 5 GHz, I wouldn't have an issue using the TL-ANT2409B antennas on both sides. I would not try to connect the people downstairs though.
You just have to be careful when using these high gain antennas. You can cause yourself and others around you all types of problems. You can also end up with this.
I know this is alot, but there are many different ways to mess up when you are trying to do something like this with other network around. I would start by downloading inSSider to see what exactly what other wireless networks are out there. http://www.metageek.net/support/downloads/