Questions on my new swarm

[monaco]

Background:

A friend called me up to come get a swarm of bees. We put them in a hive, one deep box at the base with one more on top to hide a mason-jar sugar feeder.
I think we have the queen, but am not positive.
It's a smallish swarm, a weak hive. They've had a rough start with their combs falling over and everything.

We got three frames from the swarm box, but the comb fell off in transport. They each had only partial comb - nothing like a full frame. One had a black foundation, and the other two were foundationless.
I did my best to set them back up by rubber-banding in the frames, but everything was real soft from the heat and I wasn't that successful. Other bits and pieces of comb I put out of the hive for them to harvest.

After about a week they've removed the rubber bands. I checked, and the combs are still pretty ugly, leaning over on to one another, etc. I did my best again to separate and orient them vertically but I'm concerned I'm messing with them too much. The combs are soft due to summer weather.

A month has now passed and they are still buzzing.  I am feeding them sugar syrup above the vent board, with another deep frame to cover it all.



Here come the questions:

1) Our presumption is to give them only the one deep to build up for winter. Some have suggested after about 3 weeks we should put on the queen excluder and a medium frame for honey. We presume they'll need about two years to build up enough resources to become a strong hive. What's the right thing to do as far as adding frames?

2) As I stated above, their few combs are a bit of a mess. Since we won't be harvesting it or anything, should we just leave them be?

3) I filled the rest of the deep frame with wax foundation frames. They have started drawing comb on some of them. Should we try to group the original/full/empty frames into any sort of order?

4) We have been feeding them sugar syrup because we feel like they need all of the help they can get. I have read both sides of that argument but really want them to survive the winter. Should we keep feeding them?

5) We saw a hive beetle. Should we bother with that yet? There's lots of empty room in the hive so I could see that becoming an early problem.

6) The hive bottom is screened. There's lots of orange blobs and white crystals underneath that have fallen through. I presume the orange stuff is pollen? That seems like a waste if so. The white things almost looks like crystallized sugar chunks.


Happy bee place:


Inside the hive:


Really messed up comb:


The only intact frame that came with the swarm:




Some new comb on  one of the foundations I put in:



Feeding:

[paus]

In my area it is probably best to keep feeding a pH altered sugar syrup and leave them alone.

[sc-bee]

-After a month you should know if you have a queen or not
-Yes clean it up or it will get worse
-I am no foundationless guy but the hive has to be level and it is better to start foundationless frames between drawn frames
-Yes feed if they are not on a flow and need stores and comb
-Looks like they are struggling with the black plastic- did you add any extra wax? If they have a choice and both are in the box they are going to the wax foundation.

And last what I think is most important--- looks like i see 3 frames of drawn out comb with bees. Put them in a 5 frame nuc they will draw comb and grow faster ans protect the comb from shb. Add more room when needed. For me two stacked 5 frames grow quicker than a spread out box of ten...

[cao]

1. You will need a minimum of a full deep for winter.  I prefer to overwinter in at least a deep and medium.  Forget the queen excluder for now.  The first year is about getting them strong enough to survive the winter.
2. Bad comb leads to more bad comb.  I would remove it if it is just nectar.  I would make sure it is straight if it has brood in it.
3. I would have the cut out comb grouped together to keep the mess in one area.
4. Yes they need fed to build comb and store enough for winter.  Once they have the deep filled then feed may not be necessary.
5. A single hive beetle is not a problem.  Dozens of beetles can be.
6. The orange things are pollen.  It happens with a screen bottom.  The white things are wax flakes that they use to draw comb.

[monaco]

Thank you all so much for the answers!