I crush the flakes in my hand as well. I reckon that if I'm only feeding a few flakes, the more particles there are the more chance there is for everyone to get some.
It could be that the fish don't like the gel those delica things are in. I've only used them once or twice as I find frozen cubes easier to deal with.
You will have to buy some equipment as I don't think SWIMBO would approve of you hijacking the kitchen things - a tea strainer and a cheap sharp knife. And if you happen to have a spare tile left over from doing the bathroom, that'll come in handy too. Save a small yoghurt pot or some such (I favour those individual cheesecake pots)
Squeeze the delica gel into the tea strainer and wash the gel off, and feed what's left in the strainer. When you've used it all, get some frozen cubes of bloodworm and brine shrimp. Use your new knife and the spare bathroom tile as a chopping board to chop a portion off a cube. With bloodworm, shave layers off as that also chops up the worms. Deposit the rapidly defrosting bits into the yoghurt pot and add a bit of tank water. The water goes red with bloodworm - unless I've choped the bits up so small they'd go through the strainer, I strain them then feed the bits. I also strain brine shrimp and wash to remove any salt.
If the broccoli debris includes just the tiny flower heads, yes you can try those. Microwave them in some water to blanch them first, then keep an eye on if the fish actually eat them. If they do, good, feed that again. If they don't, siphon it out before it goes off.
With peas, you'll need to mash the insides up quite small for your fish. Turn the filter off just before you drop it in, but don't forget to turn it back on 5 mins later. If you leave the filter running, it'll get sucked up before the fish can get it. Voice of experience