Unfortunately, the cost of being overweight is gaining loose skin as you lose the weight. You cannot tone up fat or loose skin. However, you can tone the underlying muscles and keep reducing the overall body fat percentage. In time, as you rid the loose skin of the tiny row of fat cells that is stopping it from shrinking back (and this IS tied to genetics and age) you may be able to firm it up. There is some evidence to support skin brushing (it increases circulation if nothing else) but do not be conned by these miracle creams and cellulite treatments, they do not work on loose skin.
No problem at all doing strength training during P1, even though many coaches prefer you not to exercise as it makes their job easier because they don't have to calculate whether you need an extra packet and keeping an eye on your nutrition levels versus your exercise level. They are trying to ensure you lose at optimal rates so that you don't quit the program, but they fail to take into account that losing weight quickly can also cause body image issues and that exercise keeps your base metabolism higher than being sedentary. Ultimately this stops your daily calorie intake level from plummeting, so when you phase out of IP you don't have to spend a few months rebuilding your slowed metabolic rate.
If you have flabby underside of the arms you need to be working your triceps (hold a weight above your head, bend the elbow and bring the weight down to where it is behind the head) and raise it back above your head. The two actions count as a single rep. Second exercise is to bring the elbow up to the shoulder, so that it's parallel with the floor. Bring the forearm up behind you til it is level with the upper arm. Or get on a Triceps V machine at the gym. Simple fact: start with low weights and do more repetitions. You should feel a little muscle fatigue as you finish the last reps. As your body becomes accustomed to it and you feel little to no fatigue at the end of the set you should increase the weight. Start low. If you struggle, decrease the number of repetitions rather than reducing the number of sets.
If you have flabby front arms, then work the biceps. Curls curls curls, one arm rows and shoulder shrugs to keep your neck and shoulders nice and strong to support the increased weights.
Personally, if you aren't a regular gym goer, I would spend the money and have a personal trainer for two sessions. They walk around the equipment and weights with you, advise you on form, recommend weight levels and reps and generally teach you which muscle groups you are working. It really helped me understand that just doing the exercise isn't enough - you need to be doing it with the right form or you risk injury and wasting your time doing something that will not build muscle strength. It helps to keep the "helpful" guys at bay, too!

Finally, you will not become muscle bound - women lack the testosterone to get into serious body building - that takes a ton of supplements and way more protein than we are having on IP.
Like Sharkie, I also do weights at least 3 days a week (more like 5, because hubby's gym routine is split over 5 days, with 1 cardio - swimming - and a rest day).
On the extra packet front - strength training is not meant to raise your heart excessively high, so provided you have eaten in the preceding 2 hours you shouldn't need to packet before the workout, but do top up after it. Keep it light - a hardboiled egg may be enough to put you back to feeling good, or half a packet or a whole packet. This may vary day to day. I don't need an extra packet for the gym anymore, but I did when I started.
On the subject of fueling both before AND after exercise, this is more a cardio trick - especially for running. Running is a constant motion and you keep the heartrate elevated for long periods of time - this means that the body either needs to have sufficient fuel for the majority of the run OR it will break down muscle to use as fuel (which is specifically what you do NOT want - the point is to spare the lean tissue and burn the fat). The way to combat it is to ensure that your blood sugar level is high enough to last at least 75% of your cardio, then top the remaining 25% up after you finish - with a boat load of water to help your muscles recover.
The body is normally reactive and it will soon tell you if you are putting it under too much strain. Be prepared to start slow and build up.