Yes. Soy contains phytoestrogens or plant estrogens. These are not the same as the human estrogen, but they have similar biologic activity. They are, however, very dilute in soy products.
Phytoestrogen. Soy contains phystoestrogen, also known as plant estrogens, a weak form of estrogen.
Not per se. Soy contains plant phytoestrogens which are weak (very weak) activators of the estrogen receptor. The word "estrogen" commonly refers to 17-beta-estradiol, the most potent of the estrogen receptor stimulators found in the natural human circulation.
No. Soy milk does not contain human estrogen, but it does contain plant estrogens.