Welcome! SBD is a great way to eat for life, not just to manage weight. And while P1 is a bit restrictive, it is primarily meant to be a cleansing period. If you have been on strict Adkins, you may already be over this hump.
Second, RELAX! This is not a frenetic sprint, it is relearning how to eat.
Okay, now to your questions, and others who have been doing this longer PLEASE pipe up here.
Desserts -- there is an allowance for sweet treats, limited by calories, during the first two weeks. There is a specific list you can get from the FAQ links under Phase One Discussion. The purpose of P1 is to jump start things and get you in the habit of avoiding bad carbs. SO pay some attention to this list. You should familiarize yourself with the philosophy and approach of SBD - eating snacks is pretty necessary. To get familiar, you can get a cheap copy of South Beach Diet supercharged (more up to date food lists, among other things, that the original book) from a library or USED from
http://www.abebooks.com. You really need to get into this because it is more than just a diet plan, it is an approach, and some things just aren't intuitive (at least to me.) Eating veggies (1 cup in the morning with breakfast, two cups minimum with lunch and again with dinner, but again, look at the list for which ones to avoid in the first and second phases).
Breakfast - eat on your own schedule! Just make sure you eat three meals a day according to the plan, plus snacks, even when not hungry. You need to stay ahead of the hunger and keep your blood sugar from spiking and crashing. It's a key to success, and snacks help.
You don't need to count macronutrients like fats or carbs, though some folks do. You don't need to weigh food. What IS important is to eat from the prescribed list, avoid the Avoid list, make sure you get the minimum amount of veggies, and yes, get off your butt and get some exercise. There ARE some foods that are limited but not prohibited -0 see the food list. Beans, for instance, are limited to 1/2 a cup, twice a day, in P1.
Transition from Adkins - So maybe you gain a few pounds maybe. So what? This is a longer journey, and if this happens, your body should quickly readjust. Trust the process. It is equally likely that your body will get a jump start from the change in nutrients and start losing again instead of gaining! I did Adkins years ago, lost some weight, and it ALL came back and RAPIDLY, as soon as I resumed normal eating. It just wasn't sustainable for me. And too expensive. You'll find veggies much less expensive than all that meat!
Crystal lite is fine. Count it.
Sodium - To the extent you're following the plan and also not including a lot of high sodium mixes (which you should look closely at anyway, as many of them contain things like high fructose corn syrup, added sugar, etc. which SBD focuses on avoiding) and have no medical reason to drastically limit sodium, SBD should be fine without counting it. I personally have high blood pressure (and diabetes) and so I do watch sodium in addition to the things SBD deals with. Everyone's journey is different.
So, get the book, read everything you can on this website, go shopping, and jump in! And again, welcome.