пьёт is used in 3rd person singular. "Horses", however, are plural and require "they" form: пьют, читают, живут, пишут. The И-conjugation will have ят (ат) as an ending: говорят, стоят, лежат, спят, видят.

It is a regular Е-conjugation verb. Ending-stressed in the Present, whereas in the past only the feminine form is ending-stressed (pretty typical behaviour).

Я пью - ты пьёшь - она пьёт.

Мы пьём - вы пьёте - они пьют.

(infinitive: пить ; imperative: пей ; past: он пил, она пила́, оно пи́ло, они пи́ли)

Not totally, just not how it is saidthese days (конь is associated with knights and/or cavalry).

«мой» and «мои» are different forms and do not even sound alike.

Лошадь ends in a palatalised consonant, so its plural does too.

The к, г, х, ш, ж, щ, ч rule applies to those cases where you cannot use this to predict the correct ending. For instance, кошка and нож end in a non-palatalised consonant but their plural ends in И. For ж and ш, it is a spelling convention (ши and жи are pronounced шы and жы in the modern language).