So I am really a noob when it comes to bike mechanics, especially when it comes to index /friction shifters and derailleurs. Are there specific index and friction derailleurs? Can someone replace index shifters with friction ones and keep the same derailleurs? How can you tell if a uninstalled derailleur is index or friction?

Index is in the shifters only ,it doesn't matter to the derailleurs . Yes you can replace index shifters with friction ones ,the same derailleurs will work with both.

Modern derailleurs are almost all designed for indexed shifting. Derailleurs from the late 80s or earlier may not be. To work properly without modification or adapters, indexed shifters must be mated to a compatible derailleur and a cassette or freewheel with the right number of speeds.

For Shimano, almost all index compatible derailleurs work with almost all indexed shifters. With Campagnolo I believe the derailleurs are made to match a specific number of speeds and the appropriate shifter. Sram MTB rear derailleurs must be used with Sram MTB shifters, but the front mtb derailleurs will work with shimano shifters.

THere are more exceptions and notable points but I am too lazy to continue.

Yes, you can use friction shifters with any derailer. It doesn't always work the other way around. As mentioned, the indexed shifter must be compatible with the derailer to shift properly.

I don't think that any of the previous answers is 100% right.

1. It's easy to determine an index shifter. It will have distinct detents that you can feel as you work it through it's motions. You can feeld the detents even if it's not connected to a derailleur.
2. Friction shifters will work with any derailleur. I suppose itls possible to find a shifter that doesn't have the travel to operate some derailleur, but I've never encountered that.
3. Index shifting means the shifter has detents that pull exactly the right amount of cable to move the derailleur over 1 cog space. For that to work everything (shifter, derailleur, cable housing, cassette) has to match. Some components match across brands and some don't. Some Sram shifters will index a Shimano derailleur and some won't. In addition to the above, the cassette spacing of different numbers of rear cogs has changed so your shifter has to match the number of cogs on your cassette.