Surrexit Dominus Vere, Alleluia!
Do you Eastern/Oriental Catholics pray Agelus and Regina Coeli or do you have other simmilar prayers from you tradition?

As far as I know, the prayers you mention are not specifically part of our prayer-text heritage. But I know some Gk. Catholics say them, under Latin influence. Just like some of us pray the Dominican rosary & the Chaplet of Divine Mercy. And there are Latin Catholics who pray the akathist to the Theotokos. Which is OK.

As a matter of fact,any prayer that gets you closer to Jesus is OK.

As shocking as it may seem to some who know my positions, I rather enjoy reciting the Angelus-in Latin no less! The WRO have it too.

The Angelus is rather late (High Middle Ages at the earliest), but that's OK. So its existence in any Eastern Church is ipso facto Latin influence. But not all Latin influences are bad.

Their are a few variants of an Eastern form of Angelic Salutation. This is the one I was taught and regularly recite:

Rejoice, O Virgin Theotokos!
Mary, full of grace, the Lord is with you!
Blessed are you among women, and blessed is the Fruit of your womb.
For you gave birth to Christ, the Savior and Redeemer of our souls. Amen.

The closest equivalent I can think of to the Regina Coeli, both in terms of content and usage, is the Magnification and Irmos from the Canons of Paschal Matins. They are taken during the Divine Liturgy for the entirety of the Pascal season (until the Wednesday before Ascension Thursday, instead of "It is truly proper ..."):

Magnification:

The angel exclaimed to her, full of grace: Rejoice, O pure Virgin; and again, I say: Rejoice! Your Son is risen from the grave on the third day and has raised the dead. Rejoice,
all you nations.

Irmos:

Shine in splendor, O new Jerusalem; for the glory of the Lord is risen upon you. O Zion, now dance and be glad; and you, pure Theotokos, rejoice in the resurrection of your Son!

Do they say these prayers because the Pope does?

I don't think any Catholic says certain prayers because the Pope of Rome says them. At least, no one I know has ever indicated to me that's the motivation.

We pray as we do for many reasons.

We pray in union with Christ's prayer.

We pray in union with the devotional and liturgical Traditions vibrantly present within the Catholic Communion of Churches.

We pray united with each other - with each other here on earth; with the souls undergoing purification in the afterlife, preparatory to admission into the full posession of the Beatific Vision and united with those who are already there.

I suspect the Pope of Rome prays as he does because of these and possibly other reasons.

Remember: it's all about Jesus, or at least it's supposed to be. When Catholic (and, I dare say, also Orthodox) activities get deviated away from that, THAT'S when we get into trouble.