Plateau-ed after 100 Ib weight loss: Help on moving further

Hey guys, so here is my situation. I am 25, South Asian Male, 5 ft 7 inches and 162 pounds, with 19.8% body fat and 26.2 BMI. I have undergone a weight loss over a period from March 2015 to now, and I used to be 260 Ibs when I started in March 2015. I am quite fit now, but still have a lot of fat to get rid of (I want to be ~12% body fat) along with some serious loose skin to take care of.
I had been generally relying on cardio (running, treadmill, elliptical) till like October 2016 or so for my results, but simply doing cardio isn’t going to help me going forward. I have been mixing upper and lower body strength training since November 2016, but I am still kind of plateau-ed and not sure whether I am doing the right things.

In terms of diet, I am a vegetarian, and try to stick to around 1500 calories a day.
- Breakfast: Greek yoghurt or protein shake + almond milk latte (~250 calories)
- Lunch: Some kind of salad or bowl with tofu (~500 calories)
- Dinner: Some kind of vegetarian entrée without rice or bread, could be a Thai curry, could be roasted veggies and tofu etc. (~500-600 calories)
- Snacks + occasional guilt treating: ~50-150 calories
- Since the last 2 weeks, I have started including one cheat-ish meal during the week; I have one meal in the week when I consume carbs (sweet potatoes or bread etc.)

Needless to say, having lost ~100 pounds, I have loose skin, but my plan is to at least get to around 12-14% body fat and see how it looks like and then check whether I need surgery or not. I especially am saggy on my back.

I would appreciate any advice in terms of the following:
- Types of exercises to focus on and building a workout routine for the next 1 year or so that can help achieve the results I want
- Changes to make in my diet
- Whether my plan for dealing with loose skin mentioned above makes sense.

I am happy with my weight loss but also bitten now by the desire to give it your best and become better and better, just that it is also getting increasingly harder day by day! Happy to answer any further questions, and thank you very, very much for your help!