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I don't understand how you would have less money? Surely, if you bought the other half you'd have to pay solicitors/mortgage/perhaps even stamp duty fees? then when you sold it on you'd have to pay solicitor, again, plus EA fees? Also look at what property is doing in your area, is it hanging around then being reduced? This wouldbe a disaster for you if you had bought the other half at the HA's estimated market value.
My former HA were a real PITA to deal with so I can understand why you would want to get shot of them and sell on the open market, just make sure you've done your sums first.
I don't know if I fully understand the question... But I think it depends on the independent valuation. In our area there is a shortage of properties on the market so valuing is hard. When we sold ours we were allowed to choose the surveyor so I made sure I choose one who understood we wanted the highest price he felt he could defend. We had to pay HA 1% which would have been less than an estate agent. Doubt we'd have got a higher price on the open market either.
You wil also need to check if you can staircase to 100%. Sometimes the s106 or the lease will state that you can't buy the whole property and / or the HA has first buy back. This is very common in popular areas eg rural high value places where new developments are generally not granted planning.
Depending on where you live and your target market, sometimes it's easier to sell it as is without buying the other share. Customers will require smaller deposits, mortgages, etc... I know somebody who staircased to 100% and could not sell it but the other properties in the same complex for sale at x% sold relatively quickly.