I do ship plenty of wine when travelling on BA so I hope to be of help.
1) You can do both. If the cardboard box is made for shipping (e.g. bottles are well divided and secured) you can ship the whole thing as is. It will indeed count as one piece of checked luggage. I did this a few times and never had problems. Should you decide to pack them in a normal suitcase, of course ONLY pack the wine without anything else in the suitcase to avoid serious damage to cloths in case of breakage. If you use a suitcase, use plenty of packing material and newspapers so they can absorb liquid in case of breakages (only happened to me once after 30+ suitcases shipped).
2) No. Fragile items are shipped at your risk, but suitcase damage (not from spilling though) will be covered as per normal shippings.
3) Not for 4 bottles worth £80, you're on the safe side!