What supplications can be made to ease a sick person's death and forgiveness from Allah (سبحانهُ وتعالى) for the after life?

Make dua' in the language which you are comfortable with.

Three important factors:

• Make Dua' at noble times like until a 3rd of the night has passed.
• Be sincere in Dua'
• Persist in Dua', do not become tired.

May Allah make his/her exit easy from this worldly abode.