The first image didn't make it.
Without seeing the actual tags, I have no idea why this is happening.
You can set picard not to rename files at all. Take the check mark off of Rename in the options menu. It doesn't change your extensions at all ever, so I don't know what you're doing there. It would have no reason to.
Select all the files in a proper album. Right Click->Edit. Make sure the album doesn't say "Mixed." If it does, correct it. Make sure "Album Artist" doesn't say "Mixed." If it does, correct it.
Edit->Preferences->Sorting/Grouping and make sure you don't have something odd set there. Default is Album Artist + Album Name. You should stick with the default.
Long story short is your albums aren't tagged to be properly seen as an album according to what you've set an album to be defined as. Correct the tags and simplify the definition of an album if needed and start from there.
Other than that, it's impossible to know what's happening without more information.
EDIT: Now that you've got the first image working I can see that you likely have an album defined as Artist + Album Name, not Album Artist + Album Name OR have not tagged Album Artist at all (in which case MB defaults to using "Artist" as "Album Artist"). Correcting that would solve half the problem. Following my previous suggestion regarding tagging Artists would solve the rest of the problem.
Those Artist tags are a mess IMO. List those files and select the first one. Right Click->Edit. Hit the [...] next to "Artist" and then the "Split" button. This will, fairly reliably, put each artist in it's own field. Display Artist can be whatever you want, it doesn't matter, but make sure there's only one person's name on each line below with whatever definition you want in the right column next to him/her. Click "Update". Right arrow at the bottom left of the screen to move onto the next file. Repeat.