First I want to congratulate you for your success. I'm a Personal Trainer an I really hate when trainers don't really know what they are doing. The worst thing is that they think they know.
A good trainer should have valid testimonials and a satisfaction guarantee.
Men's Health has pretty good routines. Search for two of the best workout creators of Men's Health:
Alwyn Cosgrove (Read his blog) alwyncosgrove.com
Craig Ballantyne (his newsletter gives you lots of workout ideas and he also has a lot of workout you tube videos look for cbathletics on you tube) ttfatlossworkout.com
Okay now get to work.
#1. Which exercises should I use for a FBW with dumbells?
You can combine upper body exercises with lower body exercises, but first try doing them as a circuit or super set like this.
Super Set 1 (perform 3 -4 sets before moving to the next super set)
A1 DB Squat 8 - 12 reps
Rest (30sec - 1min)
A2 DBShoulder Press 8 - 12 reps
Rest 1 -2 min
Super Set 2 (perform 3 -4 sets before moving to the next super set)
B1 DB Split Squat (or Lunges for a higher level)
Rest (30sec - 1min)
B2 DB Bicep Curls
Rest 1 - 2min
Super Set 3(perform 3 -4 sets before moving to the next super set)
C1 DB Rumanian Death Lift (RDL) or Straight Leg Death Lift
Rest (30sec - 1min)
C2 DB Rows (elbows in or elbows out) for variety
Circuit (perform 1 set and move to the next exercise) no rest or up to
1min rest in between each exercise
DB Shoulder Press
DB Split Squat
DB Bicep Curl
Combination exercises (Total Body) with DB
Squat and Press
Lunges and Bicep Curls
Lunges and Lateral Raises
RDL with Rows
DB Renegade Push-ups
#2. Should I stay in calorie deficit?
Remember that when you lose weight your body requires less calories per day. People over estimate the amount of calories they need when they exercise or gain some muscle.
When you weighted 245 a daily intake of 2500 would help you lose some weight but now you need less.
Try 2300 (once a week) on days you train really hard and 2100 (2 - 4 times a week) on days you do cardio only or lifting only. Also try 1800 (2 to 4 times a week) on rest days (this is hard but you will get results)
Eat lots of nutrient like lean meats, healthy fats like fish oil and nuts. Don't forget the fruits and veggies. If you train hard and eat quality foods don't worry about the calories unless you really want to.
Don't worry about losing muscle because as long as you lift weight with intensity you will not lose muscle. Use this to get the weights right 6 to 8 good controlled reps are very good, 10 - 12 good controlled reps means you should add some weight. If you can do more than 12 reps is too light.
I use this because it keeps my strength levels high and I can also increase the weight safely almost every week.
#3. Light cardio, FBW, heavy cardio, then skip FBW every other day?
I think you are ready to go with interval training on lifting days and 30 - 45min of slow cardio on resting days(preferably a bike for resting days).
Intervals are a time efficient way to train and increase your metabolism for more than 24 hours.
Slow cardio on resting days is for active recovery and burn some more calories.
#4. Adjustable dumbells and a good treadmill from where?
If you can save the treadmill money and run outside would be great. I think a bike that allows you to use your arms too like an airdyne is a better investment and is cheaper. A cheap treadmill (less than $700) is only good to walk.
You can also get a Stability Ball, some bands and a medicine ball for variety purposes. Kettlebells are good but you need to learn how to use it correctly.
I hope this helps, If you train hard and have good nutrition (don't forget Omega3 Fish oil to boost your fat loss) You should be able to lose 2 or more pounds a week. I lot of people disagrees with me on this but usually my clients drop a minimum of 12 - 15 pounds per month until they reach under 18% body fat and then the weight loss is less because there is less weight to lose.
Good luck and train hard (this means feel the fatigue not the pain)