I think most of those questions have been answered already.
Conditional Intent:
D commits burglary if he enters a building (etc) with the intention of committing (for example) theft. Suppose that one particular D needs a new television. He doesn't want just any old crap TV, he only wants a new 50" plasma TV. He spots a likely looking house and breaks in, intending to take a 50" plasma TV if they have one. If they don't have one, he doesn't intend to take anything. D is guilty of burglary because he intends to commit theft (conditional on there being a suitable item to steal).
That ought to be true for criminal damage as well. i.e. if D intends to destroy any TVs that he finds in the building, then D will be guilty of burglary even if he has no idea whether the property he is breaking into contains any TVs.
Criminal Attempt Act:
Yes, you will have to consider it...
Oblique Intent:
Is enough for attempted murder - R v Pearman, R v Walker & Hayles. Should be enough for other attempted offences although dont know any cases. Read Law Reform Consulation Paper no 183, Conspiracy and Attempt. See p 461 Smith & Hogan.
Specific Intent:
Well obviously it applies to s 9(1)(a) - the section says that you have to intend the offence. It applies to s 9(1)(b) because s 1(1)(a) Criminal Attempts Act 1981 requires "intent to commit an offence" in order to be "guilty of attempting to commit the offence". But again it is obvious as a matter of common sense, isn't it?