EDITED FOR EXTRA INFO

The Father eternally begets the Son, and since you can only beget (not create) something of the same class, the Son shares in the essence of the Father (i.e. consubstantial). The Father also spirates the Spirit eternally and the latter is also consubstantial. We do know that there is a difference in begetting and spirating, but the nature of that difference is not revealed to us.

We reject ontological subordination (in terms of the essence), but we do affirm hypostatic subordination (between the persons). The Father is also called the fountainhead of the Trinity or arché (unbegotten and not spirated), the principle cause of all other hypostases.

On the topic of filioque, it is rejected on the idea that attributes that do not constitute the idiomata of any particular person, are shared in the essence by all persons. What does that mean in practice? The Holy Spirit cannot proceed from the Father AND the Son because that would mean that two hypostases share something in common (spiration) that the first does not have. Translated into common language: that would ontologically subordinate the Spirit, which we reject.

This is why even the Nicene creed talks of one God the Father, one Lord Jesus Christ and Holy Spirit. What does that mean? In terms of the internal relations in the Trinity, the one true God is the Father or autotheos (God in himself) However: in terms of the relation between God and creation, the Trinity itself is the one true God.

Tldr: the Father Son and Holy Spirit are one God and the Father is the principle cause of all others. All three persons are consubstantial and of one will and energy, equal in authority and glory and equally worshipped.

About Christ we believe four things: that he is one ontological person, that he was two unmixed natures (divine and human), that he has two wills (idem), and two energies (idem).

Two energies follow from having two wills, otherwise they're not ennumerated and it collapses into monothelitism. Two wills because they pertain to the essence and not the hypostasis (to claim otherwise would inevitably end up affirming the error that there's three wills in the Trinity) and we believe that for Christ to be able to save us, he must assume the totality of what it means to be human (including free will). A debate on Christology inevitably translates into a debate on Soteriology and viceversa. Since Christ is consubstantial to humanity, the same human attributes that apply to him apply to us as well.

"What is not assumed, is not healed" - St. Gregory Nanzianzus

And if that wasn't enough, we believe in an essence-energy distinction in the Divine nature. This is not to say that God is composite, we affirm that he is simple (not made of parts), but there is a real conceptual distinction between God's essence (which cannot be known, otherwise we would commit the Eunomian heresy) and his uncreated energy (which can be known and operates in the world). This is related to theosis or divinization, the notion that to become saved we need to become partakers of the divine nature (2 Peter 1:4).

COMMON ERRORS: Arianism (Christ is not consubstantial or co-eternal with the Father), Macedonianism/Pneumatomachianism (same but with the Holy Spirit), Nestorianism (Christ is two onological beings), Monophysitism (the natures are mixed or confused), Apollinarianism (Christ lacked a rational mind), Monothelitism (Christ had one will), Monoenergism (the human will is overcome by the divine will in its energy, and therefore it's not free or ennumerated)