SureAI

Sometimes things don't seem to work the way they should.

I was in the False Dog and saw a purse on a table that said I could take it, but when I tried nothing happened. A table away & another purse I picked up fine.

Sometimes a door won't open that says it should even when no key is needed.

And in the Undercity I spoke to a "guard" or "enforcer" and was made to pay a 10P fine even though I had committed no crime (with apparently no other option except fight). When I did, I found myself outside of the Prison in Ark...no longer in the Undercity.

And Skyrim stops responding every half hour or so, even though I only have four small, minor mods operational.

Seems strange...at times.

The amount of coins in coin purses will be randomly determined. It can even be zero.
Some doors are closed/locked because there will be added new content in the feature, or they are relevant for the mainquest.
Guards/Enforcer will work correctly with the DLC, since they belong to the Rhalâta questline. However if you commit a crime, you should be outside of the prison (you are inside if you don't pay).

If Skyrim stops responding every half an hour something seems to be not working correctly on your machine. Could you post your specs? Have you tried lowering the settings, switching between enabled and disabled OneTweak, changed the CPU/RAM usage?
Which mods do you use?

Alternatively you could use a mod like "Optimized Textures". Which increases the performance. But it has some bugs.