Thats kinda the idea. Wondering how it would look if roof line was same as house? Also I would strengthen those posts - they are too thin. Maybe a triple posts at each corner, possibly sitting on a base detail. Hang an amazing chandelier and treat that blank brick wall somehow (maybe the sectional couch is against it) with some wall decoration of some kind above. A fire table would be great too! Put a cluster of decorative pots at that outside corner of the deck

Decks are great when the door is well above grade, but I'm not too much a fan of wood decks close to the ground. It is harder to keep their vicinity clean. That there is some drop-off in every direction & one must step down to the yard can be annoying. Wood posts are treated for ground contact, but not 2-by lumber ... so there is the greater decay potential. You're so close to the ground ... a masonry patio would be more durable and easier to integrate into the surroundings. Why ruling it out?

For where you're placing the roof, I'd tie flush to the existing roof and keep the same slope. You wouldn't be able to get the roof slope shown in your proposed illustration unless the ridge projected well above the existing roof line.

Not sure about matching existing roof now.....definitely don't like extending the plane. Perhaps it's same roof angle on the one side (furthest from the door, but lower) and has a "salt box" type roof on the left side. There are not rules about things having to be perfectly symmetrical. If you minimize the step out (4 inches say) there may be enough height for a ground level wood deck.

"Also what kinda of deck would be a better option vs the wood?"

A patio.

The look you want is not the roof line you have. If you can't accept what you have, the alternative is going to be something funky.