I'm a chemical engineer myself, plus I love to cook and love being creative, so I know exactly what you mean about homebrewing being the perfect hobby. I started out with the same enthusiasm as you, and now I've been brewing for 11 years already. Time flies... If you stick with it and are truly interested, you will learn a lot along your journey. You can start out making pretty good beer, but as your experience grows you will become capable of making better beer than anything you can buy or that your buddies can make.
Here are some things to help get you started on the right track, based on my experience. Some of these have already been answered above, but I'll go ahead and say the same things in my own words because I've already drafted it and I sometimes don't know how to shut the hell up.
First of all, you'll want to get that fermentation temperature down by any means possible! You can make some decent beers at temperatures above 70 F, but not without risk of being very fruity, alcoholic, and causing major headaches (literally). If you can shoot for fermentation temperature of 65 F, with an absolute maximum of 70 F (okay for most ales, but not lagers), you will be much happier with your final product. Stick with ales for your first couple years. Lagers are a whole 'nother beast.
If you can tune your A/C at least another 5 degrees lower, it won't solve the problem completely, but will help get you much closer to where you need to be. You can cool it down even more in many other ways. It could require some labor and ingenuity, but one fairly obvious method is to modify a little dorm fridge and add a temperature controller to get you down into the 60s (or even lower). There are details of such products elsewhere on the various homebrewing forums, and I haven't done it myself, so I won't comment further.
But even easier - If your relative humidity cooperates, you can cool your fermenter very cheaply and effectively through evaporative cooling - set it in the coolest corner of your apartment (wherever that may be), cover with a soaking wet t-shirt, set in a small tub a couple inches deep with water, and blow a fan on it. Check the t-shirt and tub every 12 hours or so and make sure it stays moist with a couple inches of water in the tub to allow a wicking effect. In my experience, this wet t-shirt and fan method should lower your fermentation temperature by around 5 degrees, maybe a tad more. Some people put ice in the tub as well, but my scientific mind is not convinced that this really has much effect. An alternative method, though, might be to immerse the entire fermenter in a tub of ice water, but you would need to add more ice every couple of hours, which is probably not the best means of temperature control, but maybe it would work. I just really like the plain old t-shirt and fan method - cheap and effective.
I would NOT add ice straight into the fermenter, because it could harbor wild yeast and bacteria that could harm your beer. It is not so easy to sanitize ice - you cannot boil it, for obvious reasons!
There are many ways to get to your desired volume. You can indeed do a concentrated boil. I did so for many years and made great beer with it. However, boiling the entire volume will result in lighter color and less caramelly flavor. So it also sort of depends on what style you are making and what flavors you want. If making a stout, obviously you don't care about darkening or deep malt flavors. But if making a cream ale, you probably don't want it to turn out brown and caramelly. So take it into consideration.
Best of luck to you. We are a good, smart bunch of guys here and will respond pretty quickly to any questions.