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When buds fail to open, there is either water stress, tiny insects at work, or bud infection. It may help to cut a bud in two and examine it closely for tiny insects. Viruses and fungi usually cause discoloration and/or distortion of the bud. Sometimes it helps to take an up-close photo and enlarge it so you can see more clearly. Since I don't know which plant is having problems, I'm afraid I can't provide specific advice.

Yes, you can transplant now. I usually take the opportunity to add compost to the soil while I'm digging. The key to success is to water all the way until winter has a good grip. Transplants need less water now than during warmer weather and longer daylight hours. Water stress going into winter is hazardous to all your plants.

There is no telling what it is, plus you don't know how old it is. Pesticides are only good for a couple of years.

Safest thing to do would be to properly dispose of it.

It's hard to say without knowing what kind of plant. Some are easier than others to tell whether flower buds or leaves during early formation.

Start with this article: https://www.gardeningknowhow.com/garden-how-to/info/plant-bud-information.htm

In order to encourage flower formation, don't use a high nitrogen fertilizer, which stimulates vegetative growth, sometimes at the expense of reduced flower formation.

I counted 13 from this list: https://digitalscholarship.unlv.edu/cgi/viewcontent.cgi?article=1006&context=sustain_pubs
I did not include those listed as semi-evergreen

They look like they need water. Since they are in small pots, it's important to water every day. They still look like they have some life, so go ahead and trim off dead flowers and plant in soil. Once in the ground they still need regular watering, but not as much as when they were in pots.