A few comments ...
First, there are several different climb concerns:
(a) the certification WAT limit climbs which are interested in height and temperature, only. If, at MTOW, you can't achieve a particular WAT requirement, then you need to reduce below MTOW to do so. WAT limits are line-in-the-sand minimum gradients to give you a reasonable chance of getting away from the runway and other hard and rocky bits as well as defeating the problem of aircraft which only successfully takeoff due to the Earth's curvature.. They have naught to do with obstacles or other operational considerations.
(b) if, for the runway on the day, at either MTOW or a lesser WAT limited weight, you still can't clear one or more obstacles by the required margin, then you have to reduce weight further in order to do so (or use some other acceptable technique, such as overspeed V2). Nothing to do with the WAT limit, solely a matter of not getting the net flight path too close to the obstacles. While folks carry on with gross and net, we really have little interest in gross - it's mainly to do with net.
(c) operational climb requirements, such as SIDs or other ATC directed requirements.
If somebody were to ask you: What is the minimum NET gradient a twin engined aircraft needs to achieve in the second segment? In this case, is it 1.6%? (2.4-0.8 correction)
So long as you keep in mind that this is a WAT requirement and has nothing at all much to do with obstacle clearance.
And so, for obstacle clearance considerations, the NET flight path has to clear obstacles by 35ft, does this mean we assume a slope of 1.6%, which clears all obstacles by 35ft?
First, the 1.6% is not concerned with any obstacles, it is SOLELY a WAT (certification) consideration. For obstacles, you run the standard net flight path analysis and adjust TOW, as you might require, to achieve the required NFP clearance from obstacles. Generally, the mishap-risk concern is mainly with closer in obstacles as, assuming the aircraft is operated sensibly, the gross/net decrement will put the aircraft well above the NFP the further out we get from the runway. This often confuses the line pilot who, knowing that the critical obstacle is, say, that hill at 3 miles, then has difficulty reconciling the observation that, at the maximum RTOW with a V1 failure (ie in training) the obstacle is way below the aircraft. How come ? wasn't the clearance 35' ? Yes, but the 35' is tied up with NFP but you might be a moderate way above GFP, depending on how you are operating the aircraft.
Your statements are all correct. Yes the net is 1.6% on 2 engine a/c and yes it clears obstacles by 35ft
No, quite incorrect. First the 1.6% is OEI, NOT AEO as might be inferred from your comment. The 1.6% is a WAT limit and knows naught about obstacles. The NFP obstacle analysis, which will keep the RTOW at, or below, the WAT limit is the thing which looks after the obstacle clearance.
Gross is what the a/c will fly actual on one engine and net is the penalty where the obstacle limitations apply for the 35ft clearance
Actual will generally be a little bit better than GFP.. The WAT net penalty has NOTHING to do with obstacle limitiations.
... will have to be mitigated with improved climb ...
That's one technique we use but not the only one. overspeed V2 (improved climb) is of little use for close-in obstacles due to the longer OEI TOD needed to achieve the higher V2.
Having gone back to classroom teaching of pilot theory subjects in recent years, I am regularly amazed at some of the wrong ideas coming up from the lower licence grades. I can only think that there is much to be desired in the quality and knowledge of the instructors along the way. Then, again, I can recall from my own airline flying having more than a few checkies pontificate in substantial ignorance on this and that topic .....
However, stick with the Perf "A". Providing you get some decent instructors, you will pick up a lot of useful gen which folks in other jurisdictions might not.