In nature plants grow and nobody cuts them back for winter. The primary reason gardeners do it is for appearances. There is no health reason to do it other than in the case of obviously diseased plants. In fact leaving the dead foliage over winter often serves as a natural mulch.

Come spring if the dead foliage is still prominent you might wish to cut it away to make room for the new foliage.

How close to the ground to cut something (if you wish to cut it at all) can be determined at the end of the first growing season. How close to the ground does nature 'cut it'? Most green perennials that die back will go underground in the coldest part of the year. If the plant is dormant it really doesn't matter how much you cut back the green plants. They come back from roots/crowns.

Chives and garlic are perennials. Chives just grow, but garlic forms bulbs which should be divided every year for best growth. In year one you plant a single clove (in the fall). In the late summer of the next year that clove is a full head of garlic and should be pulled up. Eat what you want and seperate the cloves and replant them. If you leave the entire garlic head in the ground it will continue to grow, but you end up with goofy looking garlic bulbs the next year as each clove tries to make it's own head, but doesn't have room to do so. I find that after a clump of chives gets to be 12" or so they need to be divided into smaller chunks to retain good culinary quality. Generally this means every couple years. You do not need to be gentle with chives.

Can't help with the globe thistle.

Mushrooms aren't a problem. If you don't like them, just knock them over and they are gone.

A good thread to read about whether or not to cut back perennials is the Garden Clean Up thread.

I didn't know figs could be grown this far north. Here's an interesting read. I wonder how the former owner protected the fig?
http://query.nytimes.com/gst/fullpage.html?res=9C04E4DD1631F931A25754C0A96E958260&sec=&spon=&pagewanted=1

Leave the ornamental grass for winter interest-cut it back in April. Leave the black-eyed susans for the birds.

The only way I know of a fig to overwinter here outside is to bury it. Are you sure it's a fig? I'm not sure what "scrub branches" are.

Mushrooms are probably growing on some sort of decaying wood, even old woodchips. As justaguy2 said, they are not a problem.

tj

I used to be an avid gardener. Health problems say No more.
Still, I know some things just from experience.
I think its cool that you know you are 'adopting' a garden. perhaps you could contact the previous owner for advice? Well, if not, always err on the side of do less.
Perennials, especially new ones, do better thru a first winter if left standing. If you dont know, dont cut.
All the neighborhood birdies will love your yard. Pondy