The unknown plant sounds like it's a Ludwigia Repens or a Red Rotala if it's a slimmer leaf.
As for lights it would be best if you could switch to a CFL (compact fluorescent light) it will give you more PAR for your tank which is what we measure light in but I won't go too in depth. But basically you want to look for a light that has a Kelvin rating of 6,500K or higher. 6,500K is what the sun is measured at on a clear, mid-afternoon day; best time to grow plants! Most CFL's are 6,500K but it should say on the package, also it won't mater what watt you use since wattage is just a measurement of how much electricity your light is using!
If you don't have a soil base on your tank then I suggest getting Root tabs, any brand is fine, I use API but SeaChem is always great and then I really recommend using SeaChem's Flourish (not Excel, that's co2 additive) as for a liquid fert so use both and you're plants should be great! I use 1 drop per gallon of the Flourish twice a week.
But anyway all your root plants will benefit from both ferts but swords will be the ones who really eat up the tabs since they are heavy root feeders. So whenever someone has a sword and no full co2 system or anything, I always suggest root tabs ^_^