Should I be eating excess calories in order to gain pounds of muscle even though that will increase my fat as well?
Yes. Muscle mass does contain mass. To gain any sort of body mass other than water weight requires a surplus of calories. Keep the surplus fairly minimal (200-500kcal/day over what you need to maintain current bodyweight) and make sure you're training properly, and you'll minimise the excess fat development. However, the reality that all of us have to come to terms with if we want to build any noticeable amount of muscle mass is that there will be fat that comes with that muscle mass. This is why people go through "bulk" and "cut" cycles -- they "bulk" up and gain some muscle and some fat, then they "cut" down to retain their newly acquired muscle mass while getting rid of the fat that came with it (and getting rid of even more fat than that, if needed).
what should my diet and workouts look like?
This is a loaded question, and I could very literally write out a textbook to answer your question, so I'll try to keep it short. The operative word here is "try" -- it's very unlikely that what I end up writing will be anything you'd consider a short answer.
Your diet should include about 120g of protein/day and about 60g of fat/day, based on your current weight. Eat plenty of meat (including red meat, fish and poultry -- as an aside, it makes me flip tables in rage when people treat fish and poultry as "not meat"), some eggs, about 3-4 serves of dairy, some fruit, and as much vegetation as you can find. The meat, eggs and dairy should cover most of your protein and fat needs. Consume grains (mostly wholegrains) on top of all of the above based on whatever remaining calorie needs you have.
Training-wise, I'd probably cut down on the running. A 1 hour jog will burn roughly 450kcal as an average (depending on bodyweight, proficiency and level of exertion, a typical hour of moderate intensity cardio will burn between 300 and 600kcal), and it will increase the amount of recovery your body needs. A better combination might be to go hard with the weights, and then do some light activity on your off-days -- get yourself moving, but at a level where you could keep up a conversation with someone if you wanted to. Some people recommend this based on the "fat burning" zone. I don't. I recommend this based on light activity aiding recovery without doing much to increase the appetite, and still burning some calories and being good for health. Taking the dog for a walk or mowing the front yard are both good activities to do on your off-days for this purpose, and they'll probably make your parents happy (obviously, I realise you may have neither a dog nor a front yard, but if you can get your light daily activity in a manner that's constructive, that's a good place to start).
For the resistance training, go as heavy as you can with good technique. So, just as example weights (not as specifically recommended weights at all), if you can do 3x10x100lb back squats with good form, but you could go up to 3x10x135lb with dodgey form, go for 3x10x100lb. Bad form increases the risk of injury exponentially, while at the same time reducing the benefits of the exercise. Progression should be simple: Pick a target number of sets and reps of an exercise. Let's stick with 3x10, since that's generally good for your goals, and consistent with the same arbitrary numbers I threw out above. For each exercise in your program, early on in the program pick weights that you know you can hit for 3x10 with good form. For the first few weeks, you're not going to try and squeeze out every last rep possible or burn yourself out, you're just going to go into the gym and do each set with the best technique you can offer. The first session shouldn't feel heavy. It should be hard, because focusing on great technique is hard, but you should leave the gym feeling like your muscles could do it all again. When you get your 3x10 with good technique, reward yourself by adding the smallest amount of weight onto the exercise next time, and do it again. So, if you get a great 3x10x100lb squats, next session you'll be aiming for 3x10x105lb. If you miss any reps (which will happen when you A) outright fail a rep, B) do the rep, but your form's so far off that you'd be lying to yourself if you counted it, or C) realise than either A or B is about to happen and simply end the set early to avoid the problems that come with bad form or failure), then you'll be doing the same weight again next session, and you'll keep on repeating the same weights until you get all your target reps.
Some of the best exercises to do are squats, deadlifts, bench press, overhead press, pull ups/pull downs, rows and calf raises. Other than calf raises, these are all compound (multi-joint) lifts, which are great for a couple reasons. Firstly, it means a lot more muscle mass gets used than if you did isolation (single-joint) exercises, so you get more done in less time. Secondly, and this stems from the first point, it means a relatively high amount of energy is used in each set. One set of squats will train your thighs, glutes, core and postural muscles. To get a similar effect from isolation exercises, you might be performing a combination such as leg extensions, hyperextensions and planks. That's 3 exercises to (maybe) get the same training effect as one exercise.
You may not be able to perform all the preferred exercises listed above, for a variety of reasons. If those reasons are fixable, fix them. If not, find a way to work around them. Perhaps you can't do squats but can do leg presses or lunges and hyperextensions. Perhaps you can't do pull ups but can do lat pull downs. Perhaps you can't do lat pull downs either, but can do some isolation exercises for the muscles involved.
How far away is my body from reaching my goal?
I don't know. Your goals, though clearly stated and descriptive, are inherently ambiguous, and aren't easily measurable until hindsight occurs. Your goal could be 3 months away or 3 years away. It could be somewhere in between. It could take longer. It's impossible to say, and even if it were possible to say with certainty, there's no assurance that your goals will be the same by the time you get there, since "perfection" is a moving target.
