Please help a newbie out!

[littlenewb]

So I was given an orchid from Waitrose in a gift pot by my partner and I've grown attached to it, my first little friend.

The information that comes with doesn't tell me exactly what type of orchid it is so I'd like help identifying, but my main issue is the condition of the little guy.

My main worry is how the plant is doing. My flat has no central heating and is draughty, so now winter is approaching and it's meant to be hibernation season I am worried.

Two leaves were yellow and came off when I touched them, and I took the orchid out its original plastic casing and repotted it into the bigger black part with holes and back to the big white pot in hope it would help.

As you can see some of the roots got bad, I think I overwatered it despite doing it once a week as the instructions said- so was I using too much water?

there also seems to be some buds or things growing which gave me hope- is it likely new leaves will come? I had to cut the spike as it eventually browned and the flowers fell in hope for a new bloom

and finally I've tried to cut the more problematic looking roots. I am scared though, as I don't know if it was okay to do this or if I've killed it. There's lots of green ones too.

I apologize for the photos but it's the only way I can describe the condition:

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