"...and our solicitor has sorted it all out with land registry."
This is the important part. I take it they have done a Form TP1 (transfer of part of registered property) with a map that shows exactly which bit of the property is being split off to create a new title?
"...it is structurally unsound but with full planning and listed building consent and full architectural plans to progress (and a builder)."
Did the planning permission also include use as a new dwelling, or was this just described as an annex or alterations/extensions to the existing home?
You need explicit planning permission to specifically create a new dwelling.
Once you have planning permission for creating the new dwelling then you can set about developing it.
Where can I find a single list of things I need to do to in order to make sure it is a fully independent address (I have seen some websites but most talk about finance and I don't need that), thinking utilities, council tax, do I need a letter box? Does it make any difference that the house I am buying is derelict?
After you have obtained planning permission then you contact the part of your council that is responsible for new addresses. If you google something like "XXX Council Street Naming and Numbering" you will find it.
The local council are responsible for giving your new property a street number (or name) and they will also inform Royal Mail who will then give your new house a post code.
They will also inform other council departments such as Council Tax, Electoral Registration, Building Control, Waste Management etc. so that everybody knows that there is a new dwelling.
They will also notify the Land Registry of what number they have given the new property so that when anyone looks for the title they will be able to find it. I'm guessing that, at the moment, the new title is described as something like "land to the south of house number XX, on YY street" and so the Council will let them know what the new number is.
Apart from that, the only thing that you are required to do with the house number is to actually ensure that the new number is displayed and clearly readable.
Once you have planning permission then it is down to you to sort out the utilities etc
"...it has never been connected to the main house for lots of things, has its own boiler and electricity and gas meters."
This makes everything so much easier. Once you have planning permission and received the new house number from the council and the post code, then write to the utility companies and explain that those meters now relate to a separate dwelling with number XX, postcode ABC DEF
"Will my sibling have to pay capital gains tax? ... My sibling doesn't own a property except the half they own with me of the liveable part of the property. Neither of us currently live there yet."
My understanding is that, any CGT is based on an increase in the value of the property from the date that it was inherited. So, there is only any CGT to be paid if he has made a profit above what the probate value was.
Eg, his share of the property at the time you inherited it was £200k. He sells it to you for £200k - no profit, so no CGT.
If instead he were to sell it to you for £250k so he makes a £50k profit over (21 months? two years?) then there may be CGT payable. Whether he has to pay in this situation will depend on whether he has notified HMRC that he has made an election to make this house his main residence instead of wherever it is he currently lives.
ps
"...the council panicked and asked when it had stopped being a shop because it should have been paying business rates, we were able to confirm it hadn't been used as a shop since about 1850."
This bit did make me smile.