Is it a rambler or climber, & do I cut it back now??
If it is a rambler rose you can cut it back now. If it's a climber, you will not.
https://www.gardeningknowhow.com/ornamental/flowers/roses/pruning-roses.htm
https://www.gardeningknowhow.com/ornamental/flowers/roses/rambler-climbing-roses.htm
https://www.gardeningknowhow.com/ornamental/flowers/roses/pruning-climbing-roses.htm
How much do I trim Roses in the Spring?
This article should help:
https://www.gardeningknowhow.com/ornamental/flowers/roses/pruning-roses.htm
I found this plant suffocating under 20 years of leaves and roots and vines. Can it be saved?
A good rule of thumb is to only prune up to a third of the plant back during a season. This will give it a fresh start and, depending upon what it actually is, you may see some growth from the pruning.
I have a south facing garden in a townhouse in NYC and have a hard time getting plants to live in the back portion. I also don’t know when to cut back new growth on the plants which are thriving.
This article should help:
https://www.gardeningknowhow.com/ornamental/flowers/fgen/pruning-garden-plants.htm
specific plants are supercells, mecardonia, verbena, fuchsia, and petunias
These articles should help:
https://www.gardeningknowhow.com/ornamental/flowers/petunia
https://www.gardeningknowhow.com/ornamental/flowers/fuchsia
https://www.gardeningknowhow.com/ornamental/flowers/verbena
http://blogs.ifas.ufl.edu/charlotteco/2020/09/01/target-baby-jump-up/
It would be best to wait longer for them to produce branching on their own. Forcing them to branch can cause unattractive forking in the tree structure. Heading back will also interrupt the root development and force them to send energy to branch formation.
If however, you want to shape them into shrubs, and not trees, you can head them back to force branching.
Wonder if road salt has killed them?
Perennials that bloom in summer are usually cut back in spring. Spring-blooming perennials are usually trimmed if needed after they bloom.
If they are planted near the road and salt is used during the winter to melt snow, it can have a detrimental effect on plants.
This article should help:
https://www.gardeningknowhow.com/plant-problems/environmental/salt-damage-in-winter.htm