Scales and frequency of weighing yourself?

10 lbs is totally possible. I did that in less than two weeks when I started. Getting rid of all of that extra fluid felt so good! It will slow down now, and sometimes not move at all for a few weeks. Take measurements or try on clothes that are a little too small for some extra "atta girl" reinforcement when scale weight doesn't reflect your hard work.

I weigh daily. I was someone who avoided the scale for years, and I realize in retrospect that it was part of why I gained so much weight in the first place. Lesson learned. Daily weighing to monitor my weight will be a habit.

I've learned to accept the fluctuations as part of what happens and can usually anticipate them. Heavy on the carbs or salt? I'll see a temporary gain. Same if I've added some weight to my routine at the gym. Feeling extra thirsty for a day or two? A loss is coming.

Saying that? I weigh myself naked after using the bathroom first thing every morning. When I go to the doctor, I'm fully clothed, and have usually had at least 4-5 glasses of water and 2 cups of tea--if not breakfast. All of those factors add weight. I generally weigh 5 pounds more at the doctor's office than I do at home.

I recently had to buy a new scale, and it was waiting on my doorstep when I arrived home after a recent doctor's visit. I weighed myself on it, clothes, shoes, full of water and all... and weighed the same as I did at her office. The next morning when I weighed myself, I weighed 4 pounds less.

I use the digital scale in my gym's locker room and weigh in every Monday morning right before working out (about 6:30am). I have found that I get the most accurate numbers when I only weigh in once a week as your weight can fluctuate daily. I know this doesn't work for everyone, but it has been my best bet.
Also, my boyfriend and I have a fancy-schmancy WiFi scale at home (FitBit Aria) but I don't use it anymore. I've been tempted to get on to see if there is any weight difference between the 2, but I stick to the same scale, same time each week, same clothes (I can't exactly weigh naked in the locker room, so it's sports bra and leggings!) I've lost 20 lbs in just a little over a month...to me, I feel that's an accurate measurement given the above mentioned reasons!

1) Yes, that's entirely possible that you lost that much. Spot on for how much a beginner might lose (assuming you had a good amount to lose to start with).
2) I don't think it matters if you use digital scales or not... It's personal preference. I personally use the Aria digital scale every morning at the same time after I get up, mainly because I'm lazy about writing things down, and this one transmits it directly to the app for me (which then communicates automatically with MFP). Whatever will make it so that you actually do the stuff you need to do is the best tool for you.
3) Weight loss is not linear. You will have times you'll see a big loss, a small gain, then a small loss, etc. By the time the week or month (or year) is over, the numbers will go all over the place, but the trend will be downward if you've focused on doing what you need to do. These weigh ins are all just data points to form that downward graph.
4) Honestly, I'd say the most important scale we own is the food scale. I'd recommend splurging on a "fancy" digital scale for your food ($10-$20) more than one for your body ($40-???). If you use the food scale, the other piece takes care of itself pretty well. Ours measures different types of units (we use oz, grams & lb's the most), it's big enough that you can put a small plate on it, and you can hit the "Tare" button to tell it to measure only anything above what's currently on the scale. Example: Put plate with already known ingredients on the scale, hit tare, then put on the veggies (or meat, or whatever) and measure the grams. Hit tare again, add the amount of sauce you want, and now you have the oz or grams for that. It's great.
5) Congratulations for your first 7 days, and your commitment to yourself!