Is the word sonje used for both miss and remember? Could I use it for "do you remember me" (like do you recall who I am)?

Yes it is.  And, yes you can.

Examples:
I miss you.

Mwen sonje ou.

I've missed you so much.

Mwen te sonje ou anpil.

Do you remember me?

Eske ou sonje m?

I remember I had a kitten when I was little.

Mwen sonje mwen te gen yon ti chat lè m te piti.

Ask me anything