That may be Hygrophila corymbosa but if someone else thinks differently, I won't argue as I am not always certain on stem plants. I did try this plant once, and it lasted for a few months but eventually became nothing but top leaves near the surface so I gave up on it. Once one has decided on the light, plants that do well under that light are the ones to stay with.
On the light, assuming you have screw-in bulbs (2 in the fixture), I would suggest you get yourself two 9w CFL Daylight bulbs. I use this over my 10g and over my 20g, and the plants do very well. The 9w CFL are supposedly the same intensity as the old 40w incandescent bulbs, and having used 13w, I find the 9w more than sufficient or algae becomes an issue. Get the Daylight bulbs, with a 6500K rating. You could use the warmer 5000K, I've tried both, and mixed them, but the 6500K seem to be better overall.
The sword and crypts will be good under this lighting. The Bacopa maybe, it is a stem plant and thus brighter light and more nutrients. But if it is managing now, it should be just as good if not a bit better with the 6500K CFL bulbs.
To the fertilizer, I would try a comprehensive supplement like Seachem's Flourish Comprehensive Supplement, or Brightwell Aquatics' FlorinMulti. Both are much the same, containing nearly all the nutrients in proportion. A small bottle will last you months, as you use so little.
The API Leaf Zone is only iron and potassium, and while this might help sometimes, depending upon your source water and fish food there could be other nutrients missing.
Byron.