Every autumn I trim it back to allow the gazebo cover to go on. The branches are now getting thicker and older .(it's getting out of hand) If I cut back the thicker branches will it leaf again ??!
Yes, regenerative pruning may be necessary to restore old and woody branches.
This collection of articles will give you more information on Ivy:
https://www.gardeningknowhow.com/ornamental/groundcover/english-ivy
It may be suffering from transplant shock. This article should help:
https://www.gardeningknowhow.com/houseplants/hpgen/repotting-stress-treatment.htm
I live in Florida where it's hot and humid most all the time and have a beautiful cedar pergola attached to the side of my house. I have included a picture for you to see. I want to grow some sort of ivy or plant that will climb and grow up the wood but don't want one that will grow like wildfire and end up growing all over my roof as well. Also, I don't want an Ivy that flowers and attracts bees because I somewhat remember that happening at my childhood home in NJ. Do you have a recommendation for what would be the best type of plant or Ivy to grow?
Another consideration I have found is that most vines need pruning, many twice a year and who wants to climb up high to prune them. And you may have to prune to keep it off your roof, like you say. Woody vines especially need pruning or they get very heavy and woody. Many vines are invasive as well.
For non-flowering vines, your choices are Boston ivy or English ivy, creeping fig, chestnut vine, or Virginia creeper, but they could be aggressive. For a slow growing vine think about coral vine, bougainvillea, or houseplant vines like vining philodendron. I grow coral vine and bougainvillea and don't see bees. I understand bees can't see the color red.
Here is more:
https://gardeningsolutions.ifas.ufl.edu/plants/ornamentals/vines.html
https://gardeningsolutions.ifas.ufl.edu/plants/ornamentals/coral-honeysuckle.html
https://gardeningsolutions.ifas.ufl.edu/plants/houseplants/heartleaf-philodendron.html
https://gardeningsolutions.ifas.ufl.edu/plants/ornamentals/bougainvillea.html
https://www.gardeningknowhow.com/special/xeriscape/growing-drought-tolerant-vines.htm
This is for two of my houseplants and I live in TX where the winter storm hit and I had no power or heat for 3 days and my two plants, 1 ivy and one majestic palm have frozen can I get them back?
It probably wasn't cold enough inside to do real damage unless your house temperature went below 32 degrees F. Give them a drink of water and even a light application of liquid fertilizer. Leaves may turn yellow or brown and drop. But they should regrow.
https://www.gardeningknowhow.com/plant-problems/environmental/how-to-treat-frozen-plants.htm
I think mine's called hedera ivy and leaves aren't yellow their white why are they white as I read yellow color is bad but what's white mean?
You may have a little powdery mildew starting. Here are ways to get rid of it:
https://www.gardeningknowhow.com/houseplants/hpgen/powdery-mildew-treatment.htm
two large hillsides were planted with ivy sprigs in the fall and last week my yard maintenance service completely coved the entire area with double ground hardwood mulch. Will the ivy survive?
If the mulch isn't too thick they should come up through it. If it is several inches, you may want to rake some of it aside.
As long as it is not in direct sunlight.
You can put them outside; they are hardy down to zone 4.
https://www.gardeningknowhow.com/ornamental/groundcover/english-ivy/english-ivy-plant-care.htm