The first photos in your link are pokeberry,Phytolacca americana. Many parts of this plant are poisonous. It has a deep tap root and was likely planted by a bird that ate some of the berries and deposited the seeds here.

The plant pictured above is some type of amaranth, and annual ornamental. There are also edible types of amaranth, but they don't look like this. I don't know if it is likely to self-seed and give you more plants next year.

Here is a link that might be useful: link to album

The plant with the maroon plumes is Amaranthus caudatus and the one with berries is pokeweed, Phytolacca. Both are freely seeding annuals.

Actually, Phytolacca americana is a perennial not an annual.

FataMorgana