How to Take Care of Perennials ??

I've been gardening vegetables for 25 years (which is mostly annuals), but am fairly new to ornamental gardening and more permanent plantings. I have planted a number of perennials last year and the year before, and have mostly just let them go, except for trimming back the nepeta. I am aware that some of my plants would do better with more care, but I'm not exactly sure what they all need. Do I just chop back all the leaves? Some seem to have leaves that made it through all the snow and cold. Some look completely dead, but id there life down below ground? The following pictures are by no means lovely, but will show you some of the plants I need to figure out what to do with.

First, a Geum, Mango Lassi

Here's the Crocosmia, which still had green stalks before the freeze, but is now completely brown.

And a Tiarella, with some live leaves and some mush...

An Acorus that is beginning to have a bald spot in the middle that weeds like to grow in and become very difficult to extricate.

I think this is called Aruncus (goat's beard?), but don't remember for sure. Don't know if it is still alive.

A Pulmonaria, looking kind of bedraggled, but has a few short stalks with flower buds.

A very bedraggled geranium...

A Heuchera that i just planted last Fall. Do I trim off all the older leaves or just let it be as is?

Last one for now...a little grassy thing whose name I'm not sure of. Most of the leaves are half brown but alive on the lower half. Do I trim them all back almost to the base? Pick and choose the worst to cut out?

Geums, Tiarellas, Pulmonarias, Geraniums, Heucheras: pull or trim off the funky & old leaves. Easier to deal with before all the new growth starts.
Crocosmia: I trim the stalk away close to the ground; some will pull away.
Aruncus: it is alive - trim back the stems from last year - mine are already pushing out new growth.
Acorus - you could dig it up and separate it into 3 clumps. This "weed in the middle" business fries me: weeds seem to seek out the centers of grasses & Daylilies for the sole purpose of harassing the gardener!

For trimming many of these I use tiny scissors - like embroidery shears. Easier to cut closer to the plant.

Is the last picture a Carex? If you whack it back, it's going to take a while to fill out.
Mine are looking ragged, too. I'm going to selectively eliminate some of the worst blades, and try to make it look like it did not have a tough winter!

Surprisingly, I was able to find the tag for that last plant in my overflowing box where I toss tags. You are good. it's a Carex, "Golden Fountains"

Thanks for your help, Katye. I was feeling rather overwhelmed while weeding my garden, and a little guidance on what to do with all these plants I have put in is very helpful.

I am cautiously prepping the plants for spring. I hate to cut back too much too early - just in case we have some bizarre weather event. I did prune the Japanese maple & most of my roses though - not a job I enjoy, so i had to get it out of the way.
The grasses are fine to groom, but don't whack if they're evergreen.

I have been weeding, too. Lots of weeds are surging forth & some of them are the nastiest ones to deal with. From here on out, dry days will be working in the garden days: my favourite kind.

I think Kayte covered everything, but here's another tip for the pulmonaria. Use sheers or scissors to cut back the old leaves. After blooming, you can cut the plant back again for a flush of new leaves. Sometimes pulmonarias get mildewy and this helps with that problem. The second set of leaves generally looks great the rest of the year. Give them a shot of fertilizer or compost when you do that.

Also, if that Acorus has a bald spot in the middle, it can probably use dividing. Just dig it up and you 'll see how it easily separates into smaller divisions. That will take care of your bald spot and also give you more plants!

Be careful pulling even browned foliage off plants. I've pulled many a plant out of the ground, or pulled out part of it by yanking on dead foliage. Cutting is better.

With the heuchera, just cut the leaves that look ragged off.