1st. how many frames are you using? if you are starting with no foundation, you should be using 10 frames. i like 10 in the brood box regardless.
2nd, even if you are using 10, it's important to keep the frames pushed together toward the middle of the box. that will help with that fat comb.
the stuck together frames are not a problem. take a sharp knife and cut the stuck parts.
leave the frames with brood in the middle. take the frames that are fully drawn or almost fully drawn and move them to the outside. put the undrawn frames on either side of the brood. if you have some that have funky comb, put them between well drawn out frames. if your brood frames are full, put a frame next to the brood that the queen can move onto to lay. it doesn't need to be fully drawn out, but give her one with some space.
even in your neck of the woods you have a slowdown in brood rearing, so don't expect things to get fixed overnight. you can put it the way you want it and then leave them be for a bit.
jar feeding over the inner cover is probably the easiest. if you feed in the open, watch that you are not attracting wasps, etc. while it may look to you like they have lots of honey, i do not see it. if your queen continues to lay, they will continue to need stores. unless you know that you have a good nectar flow going on now, i would feed.
your hive looks fine, just needs time and some of the stuff won't be resolved until a good nectar flow. in the mean time, they could use some building up and some stores.
you did put that piece of wax foundation back? that should be toward the center and in the future, use a frame like that to give them a guideline for starting straight.