I'm in Glasgow, but some of the principles are the same.
The "offers over" is difficult if you are not in the area - you get afeel for how much property is going for and therefore how much over you need to bid. The survey will give you a clue (you do know that you need to survey before you offer doen't you?)- but in Scotland, you will frequently over what the survey valuation is.
At the end of the day, especially in the an overheated market (like Edinburgh) you need to offer what the house is worth to you. You can get some info on going rates from the house price sites - and the Scottish Land registry is quite efficeint at getting recent transactions on.
In tenements there are a comination of things to consider: what are the neghbours like, who looks after the clsoe, how much tha annual factor's charge is eqivelant of the management charge). The facotr's charge should cover simple mainenance, as there should be enough for a small float, but anything major will then be divided amongst the flats. If a amjoirty want it, then you have to pay up. There is also now a statutory obligation (not sure what it is called) in the case of essential maintenance.
if your're looking at houses (eg a "conversion", where a larger house has been sub-divided), then simialr issues apply. Scottihs Law is different to English, in that in Scotland, ownership of the external walls, roof and foundations are shared, and therefore there is joint responsibility for all appropriate maintenance. The deeds should make it clear what the porciess is in case of disputes.
Have to say, if Edinburgh estate agents/solicitors are anytihng like the Glaswegain ones, often a house is priced low to get the interest and the procie actaiully epxted is way higher. It is worth asking the vendor what they are hoping for.
We looked at a house in Jordanhill in Glasgow a number of years ago. It was on at offer over £140k. it surveyed at £160K, PLUS the roof needed doing (estimated costs £20k). We offered £166k (I think) - and we beleieve that it actaully went for at least £219k.