"Forever in your heart" can be translated semper in corde tuo.
In Latin, "Semper in corde meo" means "Forever in my heart." An expanded version of the phrase is "In meo corde aeternaliter" meaning "You are forever in my heart."
cor, cordis means heart
angina pectoris
domino est fortillia prononounced forteeya
Cor Omnibus Indigetis
The Latin equivalent for "frozen heart" is cor gelidum("icy heart") or cor gelatum ("frozen heart").
pour toujours dans mon cœur ( mon = my, ton = your)
Clavis ad meus pectus pectoris.
Your question is very vague. Physical heart would be 'shinzou' and heart in sense of 'emotions, mind' would be 'kokoro'. You can add 'nashi' to the end of whichever you meant, to form a rough translation of that phrase.
Buaileann mo chroí go seadh
centre = centro, figuratively you may use cuore (heart, core derives from that).
imithe as an saol seo ach i mo chroí go deo