Hello Mikel, good questions. I will try to answer them somewhat briefly but it can't be done in a simple sentence or two. I realize this gets a bit technical so for others read only if you are interested. I will go into lecture mode now
Yes, keto folks largely forgo carbs (although you can't ever eliminate any macro-nutrient; we try to keep it to around 25 g per day for a true keto or in a low carb diet, closer to what I actually follow, we keep the total daily carb intake to <50 g/day). There used to be thinking, even incorrectly reported in older biochemistry textbooks, that the brain can only use glucose as a fuel. It turns out this is not true. The brain most readily uses glucose but it can also use ketone-bodies produced by the liver in the absence of regular carbohydrate intake. In addition, the body can de novo synthesize glucose from proteins and fats when it needs to and supply the brain that way as well. That is the basis of the weight loss, your body converting fat stores into keto-bodies as a supplement to your daily intake. You also circumvent the glucose-insulin-fat deposition endocrine pathway that leads the fat accumulation by keeping insulin at low levels throughout the day.
Your other question pertains to the health reasons for going keto.... Weight loss is one and a big reason I started it. I went from 5'10" 250 lbs at my peak weight to 175 lbs (I haven't lost any height

). Not all of that weight loss was from going keto. In fact the first 50 lbs was based on your standard low fat, calorie restricted diet plus a lot of exercise. I started on treadmill walking and worked my way over 3 months to jogging, then I was doing 5 km runs. This took all occured over about 5 years. At one point I became a bit addicted to running and was running 5 km daily with a 10km run every weekend. Its not that much for a real runner, but prior to that I was a couch potato for the most part. However, despite very disciplined calorie restriction and running like a madman I couldn't ever plunge my weight below 200 lbs. Frustratingly so, I also was having issues with high blood pressure and having difficulty keeping that in control. Doc kept upping my meds to control the blood pressure, it was getting to the point where I was frequently experiencing dizzy spells due to the meds and even though I felt like I had changed my life, diet and exercise the blood pressure problem was beginning to take over my life. Plus I was miserable, keeping my daily calorie intake to between 1800-2000 cal and hating every meal that I had to shovel into my mouth, as infrequent as those meals seemed. Life wasn't good for me. I had skinnier pants and looked better but I wasn't happy.
That is when I went to low carb/keto diet. It really sucks when you first start it! You experience what is called the keto flu which is basically your body having to learn how to make ketone bodies to fuel yourself in the absence of glucose. In technical terms, it takes about a week for your liver to synthesize the enzymes necessary to manufacture ketone bodies and re-adjust your metabolism. Most people lose this capacity because of the years and decades of eating carbohydrates multiple times per day and as a result your body adapts to a high carb load by not synthesizing liver proteins that aren't needed. After the adjustment period however you are good to go. After the switch I found I started losing weight again and did so pretty rapidly. At first, the weight loss is really body water rather than fat. When you use up your glycogen reserves this results in loss of body water. This occurs because glycogen (the type of carbohydrate the human body stores analogous to fat) holds 5 x its weight in water. So as you burn up that in-body carbohydrate store you literally pee out the water that was absorbed onto those molecules. After that you begin losing body fat at a more regular rate. I bottomed out and stalled at 175 lbs which seems like a good weight for me. On the IBI, I'm still slightly overweight (right on the cusp of normal) but hey I'm a 50 year old guy and always been a little bigger boned.
Health benefits. So at first, when I was peeing weight off, my blood pressure dropped right down. So much so, that I had to get off blood pressure meds because my blood pressure was too low. In part this was because the loss of body water was acting in the same way that a water pill does. I was super psyched about that (being off the meds), but it didn't last that long. Eventually, when I reached stable body weight, my blood pressure crept up again. Not as bad as when I went on meds in the first place but it was going in the wrong direction. I was able to get it under control at a much lower med dose though and it has been stable/normal since that med adjustment phase. Some people get off blood pressure meds permanently on the keto diet but unfortunately I am not one of them. Still, my dosage is much lower now and I don't have the side effects that I used to. Other therapeutic uses for the keto-diet are for Type II diabetes and it also seems to help with reducing seizures associated with epilepsy.
I can get into more technical details about mechanisms and also recent scientific literature challenging the heart-saturated fat linkage but that starts to segway and it becomes a little more indirect from my personal experience and choices which is what the question was about. As for my own technical knowledge, I am a biologist with a PhD (a university prof) but not in the medical field. I did teach human physiology at one point but my research specialty is directed towards wildlife toxicology rather than medicine. Before I started the diet my wife made me do a full literature review of the peer review literature to consider the diet before going on it. My own doctor didn't believe most of it but she has certainly been witness to my changing health stats and we're keeping an eye on my bloodwork, kidney function and other metrics. My doc actually took one of my classes during her undergrad so we have a bit of a professional candor. I think she mostly thinks I'm arrogant and full of shit, but humors me by reading review papers that I bring to her and we chat about them versus how it differs from best practice advice for medicine today. There is most definitely a shift going on in the prevailing opinions about human nutrition that is upsetting standard paradigms. It is taking society to adjust and there are also some unknowns about the keto-diet.
Sorry - that was a long post, but you asked for it! I don't necessarily recommend anybody changing their diet on my word. Do you own research, consult with professionals and come a decision about what works for you. This is only what worked for me and I'm not going to change what isn't broken.
Ken