Push Through it, you will be sore but eventually it will go away. If you really want to hop on in to an ice bath... reduces recovery time, I used to do them alot
You may not be eating enough due to the amount of calories your burning from kickboxing. bump up your cals and check back in a week or so and see if your maintaining or gaining
If you believe you have a decent base then I would Cut until your around 12% before bulking, you don't want to go into a bulk with a high BF% especially if your goal is to look lean. Its all up to...
Depends on Height and weight but 1200 is way to low, 1550 is pretty low as well, I was cutting at 1800 losing 1-2 lbs a week, you don't want to go too low on cals or else you will be losing muscle,...
Just Distribute it equally throughout the rest of the week, as long as you hit that 3500 calorie deficit /week (or however big you deficit is). Or yes, you could just carry it over to the next day if...
IMO I prefer to cut with a percentage (Ex. 20%) instead of an actual amount of calories, that way when you lose weight your not having to re-adjust your deficit.