Consider looking at things simply -
(a) the aim of heavy aircraft certification is to permit the aircraft to suffer a major failing and the crew still be able to recover to a safe landing
(b) it follows that, en-route, an engine failure (or shutdown) ought not to result either in the aircraft's falling out of the sky or getting up close and personal with the rocky bits.
(c) therefore, in the event of that failure (or shutdown) either -
(i) you can continue with a minimum terrain clearance (capability) of 1000ft (positive gradient capability just means that you can avoid going down) OR, if you can't do that, then
(ii) you can put your pre-determined descent plan into action while maintaining a minimum of 2000ft terrain clearance on the way down. It may be that you combine the two options and descend to a lower level where you are able to continue level flight
Note that the capability of the aircraft for this purpose is as specified in the relevant section of the AFM and will include some fudge factors not necessarily disclosed to the pilot.
Does this mean that:
a) obstacle clearance is 1000 ft when climbing
As a capability, the aircraft needs to be able to maintain level flight OEI with 1000ft minimum terrain clearance throughout the en-route stages of the flight OR the subsequent flight MUST be predicated on the descent and 2000ft strategy until level flight can be maintained. So one would apply this for climb, cruise and descent. In practice, for most situations, this means we look at the cruise situation.
b) obstacle clearance can be reduced to 1000 ft if the aircraft is capable of climbing (but not necessarily doing so)
The capability is to maintain level flight per the AFM data (which actually would permit a rather modest climb). It's one or the other - level flight with 1000ft clearance OR descent with 2000ft min clearance either until you are in the approach and landing phase or can maintain level flight. One presumes that, if you are concerned with real terrain clearance in level flight, you really aren't considering descending ..
As a silly example, I used to look after some Argosies (Britain's Queen of the Skies). The original AFM which came with the aircraft didn't have OEI cruise data .. so the Regulator applied some undesired operational restrictions ... and we had to jump through the hoops to modify the AFM to include suitable data. Actually, I guess that wasn't too bad as I got paid to do the work ...
Then when reaching the driftdown altitude minimum obstacle clearance is 1000ft? 2000ft?
1000ft
For the 1500ft: this is just a requirement limiting available options in diversion aerodrome (elevation)
Think of things in a slightly different way .. you really don't want to make it a forced landing from 35,000 ft .. while the Shuttle pilots no doubt derived a buzz from doing that from a far greater height, we mere mortals prefer flying a circuit ... ergo, let's give ourselves some capability for flying an OEI circuit before we end up placing the wee beastie delicately onto the runway ...
Does the driftdown altitude assures you a positive climb gradient or is this the highest possible altitude the aircraft can maintain (level flight)?
Same thing. Positive gradient just means you can stop going downhill.