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You can gently dig down and check the roots. If they are pliable still, then they are still alive. If they are brittle, it is dead and you will need to start over.

You also need to make sure that you are providing plenty of water. The plant will need lots of water until it becomes established.

This article should help: https://www.gardeningknowhow.com/edible/vegetables/asparagus/cutting-asparagus-foliage-back-in-autumn.htm

You may need to pull as much of it by hand as you can. There are some grass/weed selective herbicides available that can kill it in asparagus, but there are no organic solutions other than hand pulling. The asparagus will also need to be cut back this fall.

You may want to bring the plant indoors in your region. This article will help: https://www.gardeningknowhow.com/ornamental/foliage/asparagus-fern/asparagus-fern-care.htm

You can harvest the seeds during fall pruning. If you're starting them indoors, you would normally do this about 2-3 months before your last expected frost date. Then once they reach 6-12 inches, you can plant them outdoors, treating them like you would crowns. This article should help: https://www.gardeningknowhow.com/edible/vegetables/asparagus/planting-asparagus-how-to-make-an-asparagus-bed.htm

Most seeds are started indoors. You would normally do this about 2-3 months before your last expected frost date. Then once they reach 6-12 inches, you can plant them outdoors, treating them like you would crowns. This article should help: https://www.gardeningknowhow.com/edible/vegetables/asparagus/planting-asparagus-how-to-make-an-asparagus-bed.htm