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https://www.gardeningknowhow.com/edible/vegetables/asparagus/asparagus-ferning-out-early.htm

You should not trim asparagus unless it is dead or dying. They need to obtain enough energy to focus on the roots that are forming. Doing this will disturb that process. Here is an article for more information: https://www.gardeningknowhow.com/edible/vegetables/asparagus/growing-asparagus.htm

This appears to be normal as the plant tries to go dormant for the year. The red berries signify that you have a female plant. There is nothing wrong with this, but most people prefer males, as they are more vigorous. Here are two articles that will Help you determine when to cut these and their care:

https://www.gardeningknowhow.com/edible/vegetables/asparagus/cutting-asparagus-foliage-back-in-autumn.htm
https://www.gardeningknowhow.com/edible/vegetables/asparagus/growing-asparagus.htm

This will depend on how long it takes to dry. I would wait to water until the top two inches of soil are almost completely dry. You can check this with your finger. As far as fertilizing... You can fertilize once per year with a granular, or slow release, or every few weeks with liquid fertilizers.

Here is an article on the care of asparagus: https://www.gardeningknowhow.com/edible/vegetables/asparagus/growing-asparagus.htmhhhhh

It is best to cut them back when they go dormant. If they do not have a dormancy in your area, the I would wait until late fall or winter, when they aren't actively growing. This article will give you more information: https://www.gardeningknowhow.com/edible/vegetables/asparagus/cutting-asparagus-foliage-back-in-autumn.htm

This article should tell you everything you need to know. It covers the use of salt, an old-fashioned solution, and moves on to more modern possibilities.
https://www.gardeningknowhow.com/edible/vegetables/asparagus/salt-on-asparagus-weeds.htm