To me, it looks like you have a very old Zinc coated gate, which has many areas which have been touched up with a grey paint (I may be completely wrong)..
Typically the galvanization is done when the clean metal fence is dipped into molten zinc and effectively coated in a corrosive resistant zinc shell. if you would like to return the fence to original condition, your best bet would be to remove the entire gate and take the unit to a galvanizing plant for re-galvanizing. Unfortunately the fact that it may already be galvanized means that they need to acid remove the original coating which will cost double, and they would be worried that the acid burns into the mesh too much. (you would have to remove your lock and consult the galvanizing guys if the current hinges will be ok)
The other option is to simply remove all traces of the rust from the existing gate and re-apply a coating of paint. I would say if you choose to paint the gate do not remove, however if spraying is your intention, then i would recommend removal.
To prepare for painting. some sand paper and stainless steel brushes would do the trick, if you have some power tools you could really benefit from steel brush powertool accessories (drill, grinder or polisher)
Using some sand paper, and steel brushes (in the heavy rust areas) scrape away all rust. Once you are happy, I would apply a primer coating (zinc chromite metal primer) and then a final coat of good quality enamel paint.
The corrosion you are seeing are the zinc which has formed pots (are you near the coast?) if so... painting your fence with enamel is not advised.. since corrosion is too excessive near the coast.
another option would be to prepare the fence (sanding where the rust areas are) and then re-applying the galvanized coating with a brush. this will add some life back to the gate (but does not compare to actually having the gate professionally galvanized)
a Google search for galvanizing paint or spray should get some results.
Lastly, if you are worried about painting on the wall, simply use some masking tape on the edges.
The first step would be to strip off as much of the old paint as possible. The best way I've found to do this on stucco or concrete is to use a wire brush bit in an electric drill.
Second (and most important), it looks like you have some areas with significant cracks in them, so you'll also want to repair or fill the cracks in order to prevent them from allowing moisture into the stucco. This appears to have been the main contributor to paint failing in the past - note how all of the areas of peeling paint run along the cracks. When the stucco is allowed to absorb moisture, it gradually destroys its bond with the primer.
Finally, use a high quality masonry and stucco primer to ensure a well bonded base coat.
Best Answer
In my opinion, that's the wrong approach. Cement and mortar don't do well in places that move, and stairs tend to move.
I've restored several sets of old basement stairs in my homes, and new lumber is your best bet. I've gone with stained pine, which is beautiful but a bit soft. If you're going to paint, consider bullnose particle board.
By rebuilding with 1x8 pine and your choice of tread you eliminate those gaps, remove any squeaks (by using construction adhesive on all joints), and leave a very nice base for some good floor paint or stain and urethane.