1. If you want a more pronounced "Oatie" flavor, you should try toasting your oats in the oven at like 375 or so for maybe 20 minutes, They'll turn golden brown and you'll be able to "smell" when they're done.
2. Here's what I do for partial mashing, I hope it helps:
Do you have any brewing software? It helps, I use Beersmith. I assume you already have a recipe for your stout? Take that and put it in your brewing software, replace some of the extract with base grain. For a stout I would probably use UK 2 row or Marris Otter. My PM recipes usually end up with about 3# base grain in addition to whatever specialty grains I'm using.
So, I take that grain and put it in a nylon paint strainer bag. Then I take whatever volume of water I'm mashing in, usually about 2 gallons, and heat to strike temp as per Beersmith in a smaller pot. Then I add my bag of grains, stir good, and let it sit for the mash time I usually only do 60 minutes. The best method I personally have found for keeping temp is using my oven set to its lowest setting. I pre-heat my oven to 170, put in my "mash tun" and then turn the oven off after 15 mins. I can usually keep right around my mash temp for the whole time using that method.
Then I pull out the bag, and I usually end up putting a bakers cooling rack on top of my pot. I set my bag on that and let it drain. I'll usually use the lid of the pot to assist the process.
Then in my real brew pot, I take the remaining volume of water (for me it's 5 gal, but I think I have a bigger pot than you, so just use whatever volume you have left) and heat it to sparge temp. Then I just put my grain bag in the "sparge water" for about 15 mins. I use a black binder clip to secure the bag to the side. Then after it's done I usually drain and squeeze the same way, add my wort from the mash and conduct my boil as usual. I don't really do late extract addition, so I just add my dme at the beginning.
This is just the way I do it, I'm sure there's as many different ways as there are brewers. I know it seems like a lot, but once you get the hang of it, it's like riding a bike. I wrote this all from memory. Hope it helps.