It's been a while since I've used NMM, but it has archive invalidation built into it -- up top under the tools icon -- and applies it automatically, so there is no need to install it as a mod. If you want to make sure it's being applied uncheck it and then check it again.

RH Ironsights also requires all of the DLC, so make sure you have those or the game won't launch. You can check to see if you have FOSE correctly installed in game by opening the console with the tilde key(~) and typing getfoseversion -- if it returns a version you have FOSE correctly installed. If not make sure all of the FOSE files are in your game directory: /steam/steamapps/common/fallout 3 . . . if you have the Steam version.

If I recall correctly having to uninstall and the re-install a mod usually means the mod is already in the FO3 data folder. Usually this is caused by installing the mod and then removing it manually, removing it with another mod manager, or uninstalling NMM without first uninstalling mods. NMM scans the data directory for mods and if they are already there will generate an error message is you try to re-install them.

Get a copy of FO3edit and install it. When you run it it will stop processing files if it runs into an error. Look at the mod it stopped processing on and that is the mod that is causing the problem.

Lastly, there are a couple of ways to sort load orders. You do not have to install in a certain order -- for the most part, there are some important exceptions with advanced modding. The basic way to sort load order is to just click on the mod in the plugin window and drag it up or down to the spot you want. There is also LOOT which will automatically sort load order for you.

Good luck.