Aji Dulce is a low to no-heat Capsicum chinense (habanero relative). I've seen a variety of morphologies for it, so I can't promise what the shape would be, but generally the flavor is good like an habanero/scotch bonnet but is heatless. Some people mix them with hotter habanero types to make sauces with moderate heat, or just make almost heatless sauces with them.
Growing them would be the same as growing any other habanero/scotch bonnet relative (or just about any other pepper, really). Give it a decent sized pot and good soil, stake it and give it some support, feed it well, don't over or under-water, and it'll reward you with peppers.
A comment about having limited space: if you like hot, and if you don't have anyone in your house who you are trying to get through the gate and get them eating hotter peppers, you may not enjoy this one as much as the others. That being said, I'm sure you'll find a use for them. For example cut up fresh and in salads, pickled and put in egg salad, or roasted and included in dishes for people who might not like very hot peppers, they are pretty versatile. Pay special attention to them if they are an heirloom variety. IOW did they purchase the seeds/plant commercially, or is this a family heirloom or a pepper they brought from overseas? That might up the coolness factor a little.
Edited to add: can you take a photo of it? Just wanted to confirm it's a chinense.