Q1. Can I log in with the same account on PC and mobile?

No. PC account and mobile account are separate. But the server is cross-server.

Q2. Where do I play The Third Age?

PC

R2Games: https://tta.r2games.com/    

Steam is coming soon.

Mobile

Google Play: https://play.google.com/store/apps/details?id=com.n2pg.tta    

HUAWEI App Gallery:  https://appgallery.huawei.com/#/app/C103202265    

App Store is coming soon.

Q3. I cannot find The Third Age from Google Play/App Store/App Gallery.

For Google Play, The Third Age does not support downloads in the following countries accounts temporarily, including Brazil, Japan, South Korea, Egypt, Kuwait, Saudi Arabia, Sri Lanka, Taiwan, and Turkey.  

For HUAWEI App Gallery, The Third Age does not currently support downloads from US and Chinese accounts, subject to local HUAWEI App Gallery.

Subject to your account area.