Would this still be the case is the garage is fully finished as far as the permits? I think they've already upgraded the hvac because there are functioning air vents in the garage and I believe the electrical has already been addressed as well. The first picture is the wall I want to take down from the living room and the second is the view from the finished garage. The best way to tell if the wall is load bearing is to look at it in the attic correct?

Also, what type of material would you recommend for the frame? I'm assuming wood but are there any specifics?

An engineer can let you know about the structure. As Beverly points out, it is hard to believe that an old exterior wall (yes...a wall that separates a garage from the house even if it is shared is considered exterior) is NOT load bearing. Normally anything that is considered part of the "envelope" is structural.

For me, this is a large project. The requirements to remove that wall could be expensive and require plenty of skill from the firm that does the work (you might want to work with a Design-Build firm and not a stand-alone contractor).

I would ensure you have a STRONG budget in place before you start to open up this space. Please speak with your financial institute to see how much wiggle room you have and whether or not a second mortgage is possible.

At this point, the 4" height difference between the two space is the least of your worries. It is sooooooo far down the list of "worries" that it won't see the sun for many months.

Will the ceilings be the same height or will that have to be adjusted also?

You'd use wood framing for the structure of the floor. On a regular build you might use 2x10s for the floor structure, but since you only have to address a 4" difference, 2x4s on 12" centers are not going to work once you add subfloor and finished floor. You'll have to maybe use 2x3 framing and then 3/4: plywood and then your finished floor. Measure exactly so the transition is seamless.

Where does the sofa go once you open the wall?

Looking at the photograph of the finished Garage I can almost guarantee that the wall you are considering removing is load bearing. The span is too long not to have the wall be load bearing unless your ceiling is I beam construction or trusses.

Raising the floor of the garage with sleepers is easy but you are obviously in over your head if you are considering doing this yourself. Don't attempt a project like this yourself without getting permits. The permits will assure you are building everything correctly and not compromising the structure of your home.

Rather than take down the entire wall, could you open a large doorway between the two spaces and close the one that exists now?

I would definitely not tackle this project all on my own, I just had no idea where to even start. I live in one of those neighborhoods where a lot of the houses were constructed the same way and I've seen another house that has accomplished the same idea. When I had the house inspected they told me that the ceiling was made with joists and trusses and that because of that construction I would be able to take the wall down. I wanted to have an idea of what needed to be done before moving forward to know what I could do myself but also to have enough knowledge to keep from hiring a disaster contractor/design company. Thanks for the advice. I am attaching pictures of the example house for reference and so maybe someone will be able to tell me what they might have done to make it work?

They left the floors two different levels. I would ask them what their real life experience with tripping is.