One of the best ways to minimize the impact of pesticides on vegetables as a consumer is to plant a garden (or buy from someone with growing practices you trust and understand). That way you know most of what's going into it (other than environmental pollution and such, which is probably present in the others in equivalent amounts anyway). Growing indoors is another option. Make sure your soil has the right things in it to produce nutritious plants. Some basalt rockdust in compost shouldn't hurt to help your outdoor garden out. Other people may have other recommendations.
With apples, if your area is like mine, your major problem will probably be worms (some kind of caterpillar, probably) getting black holes in your apples. Treating that without pesticides may be a challenge, but just for the record, wormy apples are still edible (you just have to cut the part out that the worm eats through).
I recommend experimenting with tomatoes a lot. Try to grow some inside. It might be easier than you think. I've got a tomato in my bedroom windowsill (which does not get a whole lot of light) in a very small jar with a mixture of clay-type topsoil and potting soil, and it's still growing flowers after a few months. I did use a little fertilize after it looked like it needed it, though. So, I imagine with a grow light and more and better soil things would be a whole lot better. I just planted some new tomato seeds fresh from another tomato after soaking them in water with hydrogen peroxide for hours (longer than I meant to), and they germinated in just a few days. I guess hydrogen peroxide must help! I'm not experienced with eggplants or bittergourds, however.
Here are some seed sites that I enjoy (there are lots more out there), in no particular order, and which may help you if you want to garden (free printed catalogs are also a plus):
As for sticking to the supermarkets, washing is going to be good for some chemicals. Some chemicals might permeate the whole fruit, to some degree, though. However, even then, washing is probably better than nothing. What you use to wash may have a considerable impact, but it probably won't be a great help in every case.
It's good to know that even organic alternatives to synthetic chemicals are still sometimes problematic. For example, with apples, they might use copper to protect or treat the trees. You may get more copper in your diet as a result. The trees probably absorb more copper, too (so, washing it off won't be entirely effective). However, maybe you need extra copper in your diet (it depends on your levels and how much is in the fruit).
You may also be concerned about such as fungicides and anti-bacterial agents for plants, rather than just pesticides.
One alternative to trying to wash all the pesticides off your fruit would be to rinse the fruits off and then peel them. That way, you know you're not eating wax and chemicals stuck in the wax. Some food waxes may actually be healthy, but the chemicals mixed in them may not be.
Sending requests to the businesses who grow, process and sell the food is a good idea, too, I think. It may not immediately solve the problem, but it should help everyone at least a little bit in the long run.
Also, avoiding the chemicals may not always be practical. So, being healthy enough to withstand them is a very good idea. Make sure your liver and kidneys are healthy (this should help you to get rid of the chemicals when you eat them). Milk thistle and other herbs may be good for your liver if it needs help. Avoid alcohol/drugs. Get enough sunlight, fresh clean air, exercise, and other good stuff.
Another thing you could try instead of just salt water is food grade diatomaceous earth mixed with water. That chelates a lot of stuff and detoxifies considerably. It would probably help with your fruit (and maybe help to remove the wax, too, due to its texture). Just rinse it off afterward (it rinses right off with water). I've never tried this, and I doubt anyone else has either, but I think it might help, and it should be safe.
In summary, there are lots of chemicals out there that people might use, and new ones arise. You could become an expert on every single one, or you could grow your own garden, even if it has to be indoors and become an expert in something a little more cheery instead (gardening is good for you). However, if you have to get it from the supermarket, washing and peeling is probably a good idea. Live healthfully (not just as it pertains to pesticides). Maybe consider food grade diatomaceous earth with water for washing.