1 - I would pull it apart like you suggest, but leave the manure uncovered, and "turn" it every few days like you would a
compost pile, it's probably already used a fair bit of nitrogen up so that is probably why it isn't hot composting (assumption) however the matted and wet combination is causing layers of anaerobic conditions to exist, so as long as it is wet and matted, you would just be throwing in negative microbes for your garden, so i would suggest just taking the straw off and just fluffing it every so often in the sun (maybe cover with a tarp on days/nights where it is going to rain/be wet) this
should dry it out
enough and add enough oxygen to it for the anaerobic conditions to be mitigated, and the "smell" should start going more pleasant. The easiest way to tell good composted material from bad without a microscope is the smell, so once you have more of a "forest floor" odor to it, I would think at that point it would be fine to add without issue (if there is still some straw mixed in you could turn it in if you wanted to, if you have any non-composted
wood chips in it i would refrain from turning that it though)
2 - if you wanted to "reactivate" it, I would suggest making a new compost pile, and mixing bits of that one in as you build it
lasagne(sp) style, this should spread it out enough where it can be incorporated into that new pile and hot compost (you will probably not be able to do it with just that material as it's nitrogen has probably off gassed or been used up a bit already)
3 - smell is what I rely on the most, when making compost, use the wafting technique at first and if it's strong enough either pleasant or foul for you to pick up the scent with the wafting method (standing a bit back and just wafting air towards your face with your hand) then that indicates a "strong" presence, if you have to get your face nice and close to smell a foul smell, it's gone anaerobic, but is probably salvageable if you turn it then.
Not an expert or anything, just what I've learned from this site and others and what I think might help you, best of luck.
First time poster, take with grain of salt