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It might be harmless, but if you are worried about it, you can just treat the area with an organic fungicide like neem oil. That will help clear it up.

If your broccoli has yellow flowers, it has bolted and will not be of any use this season. For more information on growing broccoli and preventing bolting, these articles will help: https://www.gardeningknowhow.com/edible/vegetables/broccoli/how-to-grow-broccoli.htm, https://www.gardeningknowhow.com/edible/vegetables/broccoli/bolting-broccoli-growing-broccoli-in-hot-weather.htm This article will help with successfully growing artichokes: https://www.gardeningknowhow.com/edible/vegetables/artichoke/growing-artichokes.htm

The answer is either. Artichokes don't like standing in water, so plant them in mounds or in rows with irrigation furrows.

For more information on growing artichokes, please visit the link below:
https://www.gardeningknowhow.com/edible/vegetables/artichoke/growing-artichokes.htm

Different sizes of artichokes will grow on the same plant - this is normal. Usually the ones on the very top and center are biggest and get smaller the lower they are on the plant. They all need to be harvested before the blossoms open, regardless of their size. This article will help you determine when to harvest your artichokes:
https://www.gardeningknowhow.com/edible/vegetables/artichoke/how-to-harvest-artichokes.htm

The part we eat is from the immature flower bud. If the buds or "globes" are not harvested, then the 6-inch bluish thistle-like flower heads develop. The edible portion of the "globe" is composed of the fleshy bases of the flower bracts and the receptacle to which the bracts are attached, known as the "heart". When harvesting, you should choose one that is dark green and it should be tight and compact. Avoid those that are beginning to open.
This article should also help: https://www.gardeningknowhow.com/edible/vegetables/artichoke/growing-artichokes.htm

More water is what they need. While you may be watering everyday, it may not be enough. I would try either watering for a longer period each day or twice a day. Make sure that you are watering either in the morning or the early evening so that the plant has the best opportunity to take up the water before it evaporates.