What's your question? Ask

It is likely to be a pest problem. This article will take you to links to help you deal with this issue: https://www.gardeningknowhow.com/special/organic/

This link will help you prune these correctly: https://www.gardeningknowhow.com/ornamental/flowers/lantana/lantana-pruning.htm

Lantana is fully hardy in zones 10-11. Top growth dies back to the ground in zone 9 but will re-emerge in spring. If there have been nighttime temps below 32 F, that will ruin the foliage. It is a tropical plant and does best in warm weather. Here is more lantana information from the Sandoval County Master Gardeners: http://sandovalmastergardeners.org/plant-of-the-month-lantana/

Lantana is listed as deer resistant; nothing is deer proof when deer are hungry. Lantana is also becoming invasive in some areas so be sure to keep it dead-headed to prolong bloom and prevent spread. Some blooms produce berries that are poisonous, another reason to dead-head. This is an article from Clemson Extension Service that discusses different cultivars: https://hgic.clemson.edu/factsheet/lantana/

Yes, and this has been known to cause somewhat severe skin reactions in some people. Have care when handling the plant.

This is normal. They will die back completely to the ground and regrow in spring. You are within their zone, so they are more than likely waiting until the temperatures are just right to come back. This article will give you more information on the care of these: https://www.gardeningknowhow.com/ornamental/flowers/lantana/lantana-plants.htm

Hm... I would look to having your soil tested. This could be a nutrient deficiency of potassium or phosphorus. Either that or a pH imbalance that will appear as a deficiency.

I would recommend sending soil samples to your nearest extension service. They will be able to give you a full soil analysis. This link will help you to find the closes one to you: https://www.gardeningknowhow.com/extension-search