Wow! That was a waaay ripe kiwi - far too sweet for my taste. When I eat 'em, I just core the hard end by cutting a cone shape out and then use a peeler to take off the skin.
Ripe strawberries are also easy to core - just pull all the leaves away from the fruit and then cut a cone shape out. The core is tougher than the fruit you're interested in eating, and it'll pop right out.
Also - they seemed think people only have knives in their kitchens. I don't recommend a lot of specialized equipment, but if you're trying to prep a lot of fruit, it helps to have a peeler. Vegetable peelers and fruit peelers are different because they have different blades. Veggie peelers have smooth blades to get the best cut on root vegetables like carrots and potatoes. Fruit peelers are serrated - so they can grip the thin skin without damaging the fruit. Here's an example of a set.
For the mango and melon, I agree with @jsroberts.
Wikihow has a way of eating pomegranate that I really want to try. It uses a cold water bath to loosen the seeds - so it may be the neatest way to remove them out there! I haven't tried it, so I can't vouch for it - but I have a recipe for pom jelly, so I may be trying it.