Did you install SKSE w/ NMM? You can't do that, you have to extract the .rar (open up the skse_1_06_16 folder first, then extract) into your Skyrim directory (usually C:\Program Files (x86)\Steam\SteamApps\common\Skyrim)
If you can't open the .rar, install WinRar or 7Zip. I prefer WinRar (WinRar sometimes asks you to pay, but you can close the window and continue using it).
Make sure you installed the RIGHT SKSE version from http://skse.silverlock.org/
If all else fails, paste the SKSE log for us to read over at C:\Users\*username*\Documents\My Games\Skyrim\SKSE
I am pretty sure however, that you aren't installing SKSE right. It looks like you are installing SKSE with Nexus rather than installing it "proper". Nexus Mod Manager will not install mods that are located in the Skyrim root directory, you have to do that manually (e.g ENB's, SKSE, ScriptDragon)