Geheiligt

I've noticed my MO try to launch steam as well after upgrading to 1.2.6. My suggestion for that is to close the steam application, and also disable it from startup. Doing this and allowing MO to explicitly handle and open steam seemed to have fixed that issue for me.
 
As for skse not launching properly, I'm not entirely sure. Make sure your skse binary in MO is pointed to the skse executable and not the standard skyrim executable. Other than that maybe someone else has some better insight?

EDIT2: For some reason it looks like WB started putting my BP inside the Skyrim Data folder, instead of running through MO. I'm not sure exactly how this happened, as I have never ran Wrye Bash by itself - only ever through MO. By deleting the Bashed Patch inside the SkyrimData folder, it forced WB to create an entire new patch, which ended up inside the MO directory and show up in the overwrite folder. This allowed me to properly drag and drop the BP to my BP mod again. So far it seems as if the problem is solved. Thank you for your help!
 
I think I understand... So with MO 1.2.1, does it auto-detect and overwrite the previous Bashed Patch?
 
I may have to reinstall MO altogether. I'll try to describe the two scenario examples you gave, but with my results...
 
With my BP mod 'checked'
I run Wrye Bash through MO, rebuild the BP, close. Note that my time stamp here is consistent with what I believe you were indicating: that the original time stamp is that of when Wrye Bash was first ran -5/26/2014. There is no grey lightning bolt saying my BP mod has been overwritten, nor is there anything in my overwrite folder. This was not the case in 1.1.2. I used to get the BP esp in my overwrite folder, which I would then drag and drop into my BP mod. -This is where I am getting confused/basis of my topic.
 
Without my BP mod 'checked'
I run Wrye Bash through MO, rebuild the BP, close. Note that my time stamp here is indeed 6/12/2014. There obviously wouldn't be a grey lightning bolt in this instance as my BP mod is unchecked. However, there still is no BP in my overwrite folder.
 
I'm going to reinstall MO and see if that helps at all. Will edit below with the results.
 
EDIT: Uninstallation of MO and reinstallation via executable gives me the same results as the above. At a loss as to where Wrye Bash or MO is putting my rebuilt patch, unless 1.2.1 auto-updates the existing BP mod.
 
Update at top of post. Thank you again for taking your time to help out in this matter!