1. I hope you won't mind, if I want to make sure that your SKSE is installed properly.
When you click with the right mouse button on the installed SKSE in the left window of MO and choose the entry "information" in the newly popped up window, another window opens where you can look at the "Filetree".
Does it look like that?
> scripts > SKSE meta.ini
Here's a screenshot:
If your filetree doesn't at least show a script-folder (the SKSE-folder is manually created after the initial installation to add the SKSE.ini in its proper place), something is wrong.
In that case, I'll shamelessly point you to a post that deals with the SKSE installation procedure in MO.
2. If the installation is correct, try to start a vanilla + SKSE profile in MO: only the base game + DLCs, original inis + SKSE 3. Btw, take a look at the log that MO creates when it starts - do you get error messages?
4. If SKSE isn't working with the mentioned profile, take a look at the "skse.log"
You'll find it in: Documents > My Games > Skyrim > SKSE
Add it to your answer. If it's very long, please, delete it and start the vanilla + SKSE game anew. The new log should be much shorter.
5. Check your security programs
Make sure that no security program (antivirus, firewall etc.) has (partially) blocked the correct functioning of MO. Especially the ones that allow you to control specific processes associated with a program can turn into a problem. It's highly unlikely given your description - but checking doesn't hurt.
6. Re-install MO
If you want to be sure that your installation isn't messed up, deinstall the old one but PRIOR to that
- backup your downloads-folder (!) [very important if you don't want to spend hours downloading your mods again]
- backup the mods-folder (unless you want to re-install them anyway)
- ensure that your overwrite-folder is empty, otherwise save it
- I prefer to create new profiles but you could back them up as well, especially when you have manually edited inis for SWeetFX, ENBoost, ENB etc.
=> Don't install your new MO in program files.
7. Since Skyrim works properly, I very much doubt that its files are a problem. But you could still verify their integrity in STEAM (when I had to re-download more and more files, it was a sure sign that my SSD was dying and data corruption had set in - to name just one totally unrelated problem that can lead to files not working any longer).
But you could also click the Mod (in the left window of MO) with the right mouse button and choose the entry "information" in the window. A new window pops up. Go to "Optional ESPs" and move the esp via the arrow from "Available ESPs" to "Optional ESPs". The original ESP is still installed but not active any longer.
No, there is no such feature - and there shouldn't be one. A new version of one mod might be incompatible with another mod in your LO that was previously no problem at all; new optionals could be necessary on occasion or new patches might be needed from other mod authors, the inis might need adaptations and so on and on and on ..
Any automated system that doesn't pass the Turing Test could not do it, any that does, should not do it.