An important thread, I suggest ..
what is the minimum climb gradient that will keep you safe from terrain ( is it the 2.4% as per certification of a/c?)
2.4% refers to twin gross OEI .. such figures are minimum airworthiness Design Standard climb requirements and have NOTHING to do with terrain. Rather they impose a requirement for the aircraft to have, at the least, a modest climb capability over and above that which derives from curvature of the earth.
The answer is "whatever you need for the particular runway departure?.. ie each runway needs to have an analysis for the particular aircraft Type and Model. Rules of thumb may give you some comfort most of the time .. but there will always be exceptions to the norm. The need is for the RTOW to be restricted as, and to the extent necessary, to make the required climb profile for the runway. Strictly, gradient alone is inadequate due to the OEI climb's segmented nature - including the third segment acceleration and reconfiguration.
and how far lateraly do you have to maintain it to remain safe
The obstacle profile consideration is confined to a defined splay which you can find in your particular operating rules .. however, work on the basis that it is a fairly narrow trapezoid within which you need to remain. Ian Cohn did an interesting study years ago when he was with CASA (then DCA) .. he analysed a wealth of sim data and plotted the actual flight path tracks with an early engine failure .. a small, but significant proportion, of the departures tracked outside the trapezoid ...
MSA extends to 25nm?
The problem is the distance needed to get to MSA OEI ... eg, for a limited twin you can be looking at upwards of 50 miles to get to 1500ft .. let alone MSA. If the work is to be done appropriately, it is not a simple matter for complex terrain airports. Hence the usual desire for turnback procedures to reduce the terrain data gathering exercise
Is the airfield surveyed for obstacles in all directions when no SIDs exist?
Yes .. and, no. The typical aerodrome charts provide some information (often enough except for the more interesting aerodromes).
Some reading
here and
here
What procedures would you adopt in this situation when visual cannot be maintianed after rotation?
You do an instrument departure. The AEO/OEI procedure/tracks are defined and obstacle considerations have been addressed (for the better operators, at least). In respect of trying to wing it visually when you have terrain to worry about ... not worth trying due to the shallow climb gradients achieved in limiting conditions.
As others have suggested, not all operators do a good job in this area .. I can recall one, at least, which just ignored terrain ... working on the basis of runway limits only and AEO for the climb.