If you're so curious to know the answers to your questions, just try doing the things you've asked about, because that's the only way you'll ever know. Basically your questions pertain to personal preference, rather than laws of physics or anything that can be answered with an indisputable yes or no. Regardless, I'm gonna make an attempt here to answer your questions because I'm bored. (Warning: My responses almost certainly will not give you the answers you're looking for.)
Question #1a: Yes, you can use sausage grease or any other kind of oil, or you can use nothing if using nothing is the best way to create the kind of pizza you'd like to eat. 1b: No one can tell you whether there would be any advantages or disadvantages because what you like is not necessarily what anyone else likes. 1c: Yes, you could use sausage grease to season a pan. I'm not saying you
should or
should not use sausage grease to season a pan; I'm just saying you
can. But I think you already knew that.
Question #2a: Yes, you could use butter in the dough instead of oil. It probably won't create the same crust characteristics as dough that contains oil, but it can be done. Just try it. If you like it, then it's not only possible but it's also the right thing to do. 2b: My guess is that if you put enough butter in the dough, it will make the crust taste more buttery. But you'll never really know unless you try it.
Question #3a: Yes, decent deep dish can be made in a conventional home oven. In fact, amazing deep dish can be made in a conventional home oven. 3b: You don't need a stone, but I prefer to use a stone, and I assume most other members prefer to use a stone. But that doesn't make it the right way for you to do it. For all I know, you may prefer a pizza that can only be made without a stone. But you'll never know unless you try it both ways.
Question #4: You already know more about Pequod's than I do, but what you said sounds like what little I know about them.
You'll never know the most-correct answers to these questions unless you try these things yourself, because there are no right or wrong answers. There are no shortcuts to learning and understanding how to make great pizza (unless you just happen to get lucky and end up with exactly what you want after following someone else's recipe or instructions). Once you try the stuff you're asking about, you'll know the answers. Or maybe not, because sometimes you have to try things a few times before you have any idea whether or not you like the results.
Here's a blog post I published yesterday, which has step-by-step instructions for how to make a deep dish pizza that I think is freaking awesome. (It's also very simple.) I've included enough pictures to depict almost every step of making this pizza, and the post also contains links to related posts about things like how I seasoned my deep dish pans (with pictures, of course). Although I think it's a pretty amazing blog post about an equally amazing pizza, I realize that if I made one of these pizzas for you, you might hate it. If so, does that mean my information and instructions are wrong? No, it just means they're wrong for you. But if you love it, they're right for you. The only way you'll ever know is by trying it.
I invite you to try it.