Después De Una Muerte

Question 1

(Al principio)

My (deepest) condolences

Answer 1

Mi más sentido pésame… My deepest condolences

O Mis sentidas condolencias… My deep condolences

Question 2

First phrase: Immediately followed by either one of these:
I deeply regret this great loss OR,
I deeply regret the loss of [name]

Answer 2

Immediately followed by either one of these:
Lamento mucho esta gran pérdida… I deeply regret this great loss
Lamento mucho la muerte de [nombre] … I deeply regret the loss of [name]

Question 3

And then immediately followed by either one of these:
I am with you in this moment of grief
am with you in this difficult moment

Answer 3

Te acompaño en este momento de duelo / de dolor… I am with you in this moment of grief
Te acompaño en el sentimiento… I am with you in this difficult moment

Question 4

He must have been a great person

You can count on me for what you need

Answer 4

Finally you can close with these two phrases, in exactly this order:
[Nombre] fue una gran persona a quien he tenido la dicha de conocer…
[Name] was a great person whom I had the pleasure of knowing
Puedes contar conmigo para lo que necesites… You can count on me for whatever you need