Fresh start, trying to get back on my feet, am I doing things right?

*I hope this is not a TL;DR post, skip the first and the third paragraphs if so*

*My story and eating habits:
Hello, I'm new to some stuff and am not sure if I put up my exercise plans well, so I need some help and support. Hope I'm writing under the right forum topic.
To tell my story shortly, I had been doing yoga daily for around half a year (plus years of practicing it rarely), but stress, fatigue and lack of time somehow made me quit it in august, then I had a mild surgery a month later with 3 weeks as minimum recovery time, and caught some bad virus or something after, so two more weeks without any exercise and minimum immunity levels - and I ended up getting sick every two weeks or so, barely managing to keep up with my schoolwork while still having to go to work twice a week. Lost half my hair, gained skin issues, gained 10kg. Now it's christmas, I'm taking an academic break to try to return to my normal lifestyle, as all that laying around doing nothing made me a earweak, lazy-*kitten* stressed out 21 year old with depression.
So I'm gonna work out to get back in shape, untill I can continue being a happy hippie yogi and get back to school. My eating habits would be very fine, by the way, if I just stopped overeating and cut out halva out of my regime, as I'm a vegetarian-half-vegan hippie who doesn't really eat processed foods etc., and could spare myself by only treating myself to a bite of dark chocolate on a craving or rarely eating any sweets at all, but I recently became a halva monster as if I have a craving and buy some halvah or simply just find some at home, I consume it all in one go, which is usually a 200g or 300g piece - and I've even eaten 500g in one day twice. I can also eat some triple portions(of healthy meals) if I'm on my period, during full moon, if I'm having a marathon of drama/movies watching or simply have some free time untill my next schedule. So I definitelly still need to work on my meal plans since during all those months of being a sickly couch-potatoe I ended up stuffing myself with some of the stuffs I don't want in my body at all. I'm only a step from my ideal eating habits so I'm sure that one won't take long to overcome.

*The reason for this post- my questionable exercise plan:
I've only just started doing strength training a couple of days ago, when I bought 2 dumbbells, 2kg each. For now I'm doing 10 minutes of strenght training a day (planning to increase that to 20-30 minutes and have a few days off every week, especially since my 8 hours at work are usually kinda like a triathlon or whatever you call it. the 2-minute walk home becomes a 15-minute walk cuz I ache and all.. and then I end up having a late-night meal since it's 1:30am by the time I'm home from work, and then I might not sleep at all if I have an early schedule since no war could wake me up early), hullahoop 20 to 60 minutes a day, planning to jump rope for some amount of time about twice a week (have to have certain conditions for that one), not sure yet, haven't tried jumping rope for at least 7 years, and was never good at it, but hope to improve and have this exercise stay with me during the years, even if just occasionally. Also have low lung capacity due to being a smoker (might drop that one habit, not sure if I really want to). Will continue to try doing yoga sessions whenever I feel like it and have time for it, since even my current exercise routines steal more of my precious time than I'd wish they did- and make less impact than I wish they did, too.

*Some stuff to take note of - mostly crazy facts -
I hate intense workouts. I used to love intense yoga sessions, will love them as soon as I regain my ability to go trough with them, but I hate all the other intense, sweaty exercises that seem so unloving, so harsh. Also, it's winter now. I love walking, I could just go out and walk all day, or I could go on a 2-hour session of walking in a very fast tempo, but now it's too cold to have a five minute walk, it's wet, about to get slippery as heck (that's when I really become a hermit crab. Feels better staying home than trying to go somewhere, walking like a crab, and still being in danger of an accident that will break bones on every corner. ANd it's not pretty at all, winter in my country. Taking a walk during winter increases my depression levels most of the times). :DDD Oh also I naturally drink plenty of water, which is up to 3l a day, but I also drink up to 2l of my special teas so the more tea I drink the less is my need for water, but overall it's always enough or more of both. "special tea" meaning has a wide range of choises, so it goes from green tea upgraded by spices, to turmeric tea (also usually withsome cayenne or cinnamon), to some occasional garlic tea, and my recent favorite is lots of parsley+some green tea leaves+turmeric powder, around 3tbsp,+ cayenne powder, 1to3 tbsp, something like that in a litre of hot water. I added a few cloves of garlic once recently, that batch wasn't tasty, and I usually brew the same ingredients twice before replacing with fresh ones.

How does my exercise plan seem to people who know better? What should I correct?
I'm trying to lose those 10kgs fast, -15kg would be perfect, but I'm not that crazy and I'll be at the medically perfect BMI, close to my perfect weight enough after losing 10 (which is the amount I gained during this fall anyway). I'm giving myself 2 months at most, I don't care if some may laugh while commiting to crazy "10kg in one week" diets or if some might say that 1kg a week is the most I should ask of myself.
And I want to regain my strength (and gain more strength and endurance than I had, what I can offer a few additional months for) so that someday I could return to my healthy lifestyle, upgraded.

So if I consumed around 1200kcal with my kind of diet (veggies, fruits, no cooking with oil, no processed foods, no white flour, I also don't like eggs, don't really eat any dairies except for occasional cheese days when cheese goes like halva does. not gonna be buying halva anytime soon:D and gonna try not to notice the delicious cheese stock-ups in my family fridge) and if I kept up exercising similarly to the plan I wrote down, would that be too less, enough, or a strech while trying to reach my goals?