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Try neem oil. It is safe and effective. Here is more information: https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

It sounds like it may be grey mold. This article will help:
http://flowers.about.com/od/Pests-And-Diseases/p/Get-Rid-Of-Fuzzy-Grey-Mold-On-Flowers.htm

Yes, they produce seeds and will oftentimes even re-seed themselves in ideal conditions. You can simply let the blooms fade and then cut the dried, spent blooms from the plant. Place them in a brown paper bag. When you are ready for planting next season, just gently pull the dried petals off and the seeds can be easily removed.

Give them time to mature. In a few weeks, 4-6, you will see differences in the heights. Are you using the fertilizer according to package directions? Over fertilizing is worse than none.

Yes, any plant you have in a container should have adequate drainage, so if there are no holes in your pot, then it is best to add some.

This article goes over basic marigold care: https://www.gardeningknowhow.com/ornamental/flowers/marigold/growing-marigold-flowers.htm
If you don't think there is anything cultural that is killing the marigolds, there might be some disease in the soil, or some other problem with the site. Try growing something else in that spot.
You can also try to get some analysis of the soil. http://mastergardeners.org.uk/get-involved/find-your-nearest-master-gardener/ will give you some assistance with that.