I still have some full honeycomb from the cut-out. Would putting the shallow super back on with frames loaded with their own honey be good?
At this point I wouldn't. My concern is that there aren't enough bees to cover all the frames and protect the honey from robbers and beetles.
Or a chamber that they could access from inside the hive to get to honey and/or water?
As a general rule, feeding inside the hive is always better. Open feeding carries several serious perils. Firstly, it encourages all the bees within 3-6 miles to congregate at your feeder, causing you to waste feed on bees who aren't yours and don't need it, and encouraging disease and parasite spread between colonies. It also encourages robbing in your own yard, because when you remove the feeder, all the random bees who were used to finding food there can easily switch over to robbing your colony when there is no more syrup to be had. Perhaps worst of all, you can contaminate your neighboring beekeepers' honey supers with sugar syrup, which will never turn into honey. This is why you (almost) never feed if there is a flow on, because you don't want sugar water in your honey either.
There are many different styles of in-hive feeder available, but the easiest one is a mason jar. Just punch a line of holes in the lid, fill with sugar syrup, turn the jar upside down on the hole in the inner cover, and place an empty box over the jar. If you don't use an inner cover or don't have one with a hole, you can just place the upside down jar on the top bars instead. The risk is that the bees will build crazy comb in the wide open space of the empty box, but there are ways to mitigate that risk.
The basic reason I think you should feed is that if you aren't expecting any more flow where you live, this hive will not continue to grow, and I don't think that colony is at critical mass to make it through the winter. But then again, your winters are pretty mild, so I'd like someone from your climate to confirm that I'm thinking correctly. Where I live, I want to see 2 of my boxes (8-frame mediums) crammed with bees going into winter. I know your girls are in a deep, and that it's not fall yet, but that colony just looks sparse. All of my colonies are in at least 4 boxes right now for comparison.
Guys, he is feeding in "fall", but his goal is to continue to encourage brood-rearing, so do you think 1:1 or 2:1 syrup?
What about water ? It seems like they would need water, but I know nothing here..
Bees absolutely need water. Like basically every other living thing, they need water to drink, but they also use it for their air conditioning. Bee spread water on the combs and then fan their wings to encourage evaporative cooling. Unlike feeding, open watering is perfectly fine. Bees are at great risk of drowning in deep (for them) standing water, and they also love "dirty" water, so they really like the edges of bodies of water or puddles. If you have somewhere on your property that is always wet (like a leaky hose or if you have drip irrigation or a boggy spot that is never dry) they are good to go already. I don't, so to be sure they always have access to water when it hasn't rained, I have an old rubber dog dish full of stones in my mom's garden, and she makes sure it is always full.
