I wouldn't recommend Keto or any "diet" to someone new to fitness who's just looking to shed a couple of pounds and get in better shape.
Yes, except that HIIT can be changed to any form of cardio or even completely excluded.
1) Use an online calorie calculator to find out how many calories you're burning per day.
2) Sign up at Myfitnesspal and start logging what you eat. Set your calorie goals at 500 less per day than what the calc in step 1. Hit those goals with something like 30-40% protein, 30-40% carbs and the rest fat. You might want to get a food scale so you can be precise. Most people can only start eyeballing and make good food decisions after they have some solid experience. Do not exclude any macronutrient; simply eat well balanced meals with protein in every one of them and good carbs and fats. Cut out all refined food such as bakeries, white bread and the like.
3) Start a lifting program and log your workouts. You might want to try something like "Stripped 5x5".
4) If you want to, you can do some type of cardio. Rest days is best, but you can also do it on the same day as lifting if you have a couple of hours in between. Wahetever cardio you do, it shouldn't affect your lifting negatively. If it does, cut it down or remove it all together. Cardio can just be walking for 45 mins.
5) Track you body recomposition. Use the mirror, a scale, bodyfat calipers or a measuring tape. Adjust calories down or up if you're losing too fast / too slow. You should be able to lose a pound a week if you do 500 calorie restriction per day. Btw, if you're new to lifting, you may very well be able to build muscle and lose fat at the same time which means that the scale weight will not change much.