The ethernet port on my Raspberry Pi 2 is damaged, can it be replaced?
If you mean replace with another solution, yes. You could use a USB-Wired Ethernet adapter. I'm using TP-Link adapters and they work quite well.
If you mean physically repaired, while it's not impossible, the effort will likely cost more than the price of a new RPi 2B or require specialized skills. The RPi additionally needs integrated magnetics, so it's not just a simple RJ-45 jack replacement. See this article for a description.
Yes, but you would need to:
- Know how to desolder, and be able to do it carefully. There are 8 datapins on the jack, plus 4 pins (2 for each) for the LEDs, plus 2 tabs on the side. So 14 connections to desolder.
- Buy a new jack. The ones used on the Rpi are made by EDAC, Inc (at least on my RPi2), and this item on DigiKey is the closest one I can find. With shipping inside the US this will set you back ~$11 for one. Note that it has special tabs on the top and the side which seem to be made for holding it in place inside an enclosure - these might lead to an incompatibility with RPi enclosures, but maybe they can be removed ...
- Solder on the new jack, making all 14 connections correctly.
All in all, this is going to cost you money - (about 1/3rd of the price of a new one) and lots of time (Unless you're a (de)solder wizard, at least an hour of desoldering+soldering+prying the old socket out). As Bobstro correctly mentions, buying a new one might be a faster alternative, or using a USB-Wired Ethernet adapter. I have a UTechSmart lying around which I bought for $12 on Amazon.