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I have linked to an article below that will explain why these tillers or "suckers" are happening. The recommendation is to leave them be as there is no evidence to suggest that they impact corn yield and they "may" actually produce ears of corn themselves.

http://www.agry.purdue.edu/ext/corn/news/articles.03/Tillers-0623.html

These articles will help with growing corn: https://www.gardeningknowhow.com/edible/vegetables/corn/how-to-grow-corn.htm
https://www.gardeningknowhow.com/edible/vegetables/corn/grow-sweet-corn.htm

The wood shavings should be okay as long as they are not fresh, which can burn the plants.

It would be best to compost the shavings/sawdust prior to using it in the garden. Not only will this allow it to age, which will lessen the chances of burning plants, but it will also prevent it from taking up too much nitrogen from the soil. This article might help: https://www.gardeningknowhow.com/composting/ingredients/using-sawdust-in-your-compost-pile.htm
If you have already added them around your plants, I would either remove it or work it into the soil and replace the shavings with straw mulch. This will retain moisture and keep the plants insulated.

It would be possible for a corn plant to do this.
I could be 2 kernels next to each other emerging.
It should not be a problem.

https://www.gardeningknowhow.com/edible/vegetables/corn/how-to-grow-corn.htm

They may not be getting enough water. Corn has very shallow roots and needs lots of water during its active growth, especially in temps as high as you are experiencing. Typically, the garden needs about an inch or so of water each week. It is a good idea to water deeply (for about 20 min. or so) every other day or two, depending on the weather. Once temps reach 85 F and up, daily watering is often necessary.

It is possible, but it may also be caused by a lack of nutrients. Have the soil tested. It may be a phosphorous deficiency. Purple leaves/foliage are a sign for this deficiency. Regardless, adding a little phosphorous will not hurt the plant. Here is more information: https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/phosphorus-plant-growth.htm

As for the birds, netting works for fruit trees and such. I am not sure how or if this would work with your corn plants, but it may be worth a try. The methods in this article may help with protecting your plants as well:
https://www.gardeningknowhow.com/edible/fruits/fegen/protect-fruit-tree-birds.htm