What summer flowers can be planted in northern India in March? The summers are humid and very hot (35 °C average temperature). My garden is covered by a translucent FRP sheet (Fiberglass Reinforced Plastic) so the plants receive medium sunlight.
Many tropical plant varieties would grow happily in this type of setting. It all depends on the mix you are looking for. You should try to consult with a local agricultural college, and speak to the nurseries as well. To date, my mother consults with TNAU in Combatore and the local nurseries and the recommendations usually pan out quite well.
I would make recommendations for monocots like the Birds of Paradise, Strelitzia reginae and variants of Musaceae you can get. This page appears to offer a nice mix of angiosperms: http://www.theflowerexpert.com/content/aboutflowers/tropical-flowers
They also have some bulb varieties. Of course, you are going to be dependent on what local nurseries carry, so do talk to them. You can compare what grows in Florida, US and that should be comparable, since Floridian summers can be quite hot and humid as well. Parts of Kerala get quite humid too, so you can look to what grows well there for comparison.
In general, Marigolds, Oleanders (the fruits are poisonous to humans and cats, so beware) and even some hardy wood roses will do well in the bushy variety. You should see if Cestrum nocturnum (colloquially, Raat Ki Rani) will grow well in your area (ask or see this in people's houses in your neighborhood - another great way to steal planting ideas). We have had one in my home in Coimbatore for ages and it is one of the most exotic, wonderful things that endeared me to botany and gardening. Hibiscus rosa sinensis, or generally Hibiscus, should grow well.
Similarly, you might be able to mix in a succulent, Epiphyllum oxypetalum - another night flowering plant which my mother and I successfully grew and waited till midnight to watch it flower.
In terms of variety, it comes down to how much space you have. If you have space for trees, several varieties of Fabaceae should grow quite well. Many varieties of Liliaceae ranging from the Jasmine to many exotic varieties should grow fine. I would also recommend Neem, Azadirachta indica if you have space for deep roots. And in that shade, you may be able to grow some plants.
Bougainvilleas will grow quite well in hot, humid conditions I believe. Geraniums, if you can get them in nurseries would grow quite well - they can adapt to almost any condition on this planet.
NOTE: Several of my recommendations above tend to attract snakes. This includes the Bougainvilleas which attract snakes that want to use the thorns to shed, so be advised of that.
You could definitely grow many varieties of Cactii and succulents, which adapt quite well to quite a variety of climactic conditions. Some succulents like the Jade will flower in winter, making your garden look interesting round the year.
Hot, humid weather might be too much for varieties of Crotons, but look for hardy ones in nurseries. Or, try to see if any varieties of Pittosporums will grow in your climate. It is good to mix in color foliage, as they can offer a nice complementary color splash.
Lastly, you could also experiment with a green house and try varieties of orchids.
Depending on the mix you choose, you can get flowers or color throughout the year.