7" is not a specification for shallow rooted. Most plants, 95% of all plant roots are in the top 6" of soil. Flowers and fruit production should be discounted as reproductive growth needs far far more light than a kitchen window. I would focus on ONE plant, not a few different plants as that will make the PUNCH of your project far greater than a discordant mishmash of different plants.
My suggestion would be Orange Sedge...a lovely grass that would get a foot high that you could trim once in a while like hair; make a ponytail straight up from the center of the potted plant and cut off a few inches. Lovely. Soft yet formal. No flowers you will notice but the bright green streaked with bright orange color. This is considered an ornamental grass, and I love it for pots and have always wanted to try this in my kitchen window (that I do not have right now).
You have to use JUST potting soil. No garden soil allowed in pots for potted plants. Raise the bottom of your pots a 1/4 inch off the surface or saucer using bits of tile. Dump excess water. Do not over water; allow to dry out in between watering. Make sure you use a little FERTILIZER. Osmocote 14-14-14 would be perfect. Purchase as one gallon plants from a nursery. Sometimes you might be able to find 4" plants. Consider using a plant TROUGH, a rectangular pot (clay is best, honest) with a tray and you might even want to purchase POT FEET...cute. Nothing but potting soil in the pot. Nothing else added, no rock or gravels at the bottom of the pot. Nothing but vines would provide total shade through that window and they get pretty leggy. This grass is soft and blows in the wind of a desk fan. Beautiful.
EDIT: A sweet little Lorel bird pointed out that I had misread your question. I sure did! I am so sorry. I am attaching my favorite vine as another idea for the OUTSIDE of your window. Grills usually go on the outside?
This vine will need some work on your part because where I've grown it we had winters. You don't, lucky you. This vine's only drawback is that it can grow very quickly very big. Lovely shade, there is not a more hardy vine to my knowledge. It is a perennial so you will have to chop it down once or twice per year. It is a yummy lime green golden color (that changes to dark green in the late summer where I've grown it) and it is called Golden Hops. The flowers are prolific...delicate, dried, Japanese Lantern looking flowers. Yes, you can make beer with this plant and it was wonderful. You do have to chop it down once in a while so it doesn't cover your entire home. Golden Hops
My second choice would be a Kiwi, Actinidia kolomikta, the male boasts green, white and dark pink foliage. Arctic Beauty Kiwi Because you don't have winters you will have to keep this vine from taking over as well.
A third choice would be Bougainvillea Bougainvillea
These three plants I am assuming would be planted in the ground below the window. If you are wanting to plant in a window box a more tender vine; here is 24 to choose from; 24 climbing plants for pots When planting in a pot, even in the Tropics (you lucky dog...I've got cabin fever badly) you MUST use sterilized potting soil.