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The branch collar is the joint where the branch joins the trunk or another branch.

Here is a link that has a great image of these points on a tree.
http://fyi.uwex.edu/forestry/when-is-the-best-time-to-prune/

Hmmm, can you let us know what type of flower that your are growing?

Flowers that are done blooming generally have a shriveled appearance.

Lilac's are best pruned in the spring, following their bloom period.

Pruning of most shrubs will depend on if they form flowers on old or new wood.
It is best to research the information on each plant type specifically.
Use the search tab at the top of the page for articles about your specific plants.

Here is a link about Lilac pruning.

https://www.gardeningknowhow.com/ornamental/shrubs/lilac/pruning-lilac-bushes-when-to-trim-lilac-bushes.htm

Pruning can be done following blooming. If the vines have become woody, these, the pruning can be done in stages. Prune 1/3 of the plant each season to gain control of the vine.
You can also cut the entire vine down and start with new plants. You can take cuttings very easily from your plant.

https://www.gardeningknowhow.com/ornamental/vines/black-eyed-susan-vine/black-eyed-susan-vine-care.htm

It is possible to prune your plants back now without hurting them, but this will remove the flowering wood, so you won't see any flowers next year. Your other option is to wait to prune them next year. Deutzia can also benefit from the removal of about 1/3 of its stems down to near the ground. You can do this anytime, and it will encourage more healthy growth the following year.

Here are some possible reasons your Deutzia may not have flowers yet:
https://www.gardeningknowhow.com/plant-problems/environmental/plant-not-blooming.htm

There are several factors that go into pruning; how and when.

The type of plant or tree is most important along with your growing zone.

Many trees and perennials do require or is best to time pruning while they are dormant or just prior to leaf break. This is not always the case, such as Birch Trees. Birch Trees should be pruned in Summer.

Many blooming plants should be pruned following first bloom, so pruning in Winter or Early Spring will result in removing the seasons flowers.

If you can give us more specifics we would be happy to help you with your garden.