What's your question? Ask

The picture was too dark and too far away for me but it is either aphids, scale or mealybugs (a cousin of scale). I suggest taking a sample to your local garden center in a sealed, transparent, plastic bag for identification.

Your plant may be the victim of fasciation. Here is more:

https://www.gardeningknowhow.com/plant-problems/environmental/fasciation-in-flowers.htm

Yes, you can deadhead them at any time. Since they are in full sun, and it's probably pretty warm there, I would water every other day to start. Then, depending on whether you get rain or not, and the temperature, keep them watered enough to prevent wilting of the flowers. If you wait three days and they wilt, then that is too long. Water every two days, etc.

This looks to be an infection from overwatering, unfortunately.

Pruning any heavily infected growth, along with a fungicide and proper watering practices will help. These articles will offer more information:

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/test-soil-for-pests-and-diseases.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm

https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

https://www.gardeningknowhow.com/garden-how-to/info/what-is-copper-fungicide.htm

I think that may be a bacterial disease called Aster's Yellow and spread by leafhoppers. Most people put them in the trash as there are no controls.

Pick the black berries and the seed will be inside. Lantanas are hybrids so the results won't look the same as the parents.

https://www.gardeningknowhow.com/ornamental/flowers/lantana/how-to-propagate-lantana.htm