Let’s learn about "사진 찍자” from Naver portal

함께 (사진) 찍자 (To the younger or friends)

함께 (사진) 찍어요 (Regardless age)

함께 (사진) 찍어실래요 (Regardless age)

함께 (사진) 찍읍시다. (Regardless age)

==> Let’s take picture together

1. is it 찍으실래요 or 찍어실래요

2. @캬라멜 함께 (사진) 찍어실래요 is right

That means "Shall we take a picture together"

함께 사진 찍어요 : Let’s take a picture together

(사진) 찍을래 : I want to take a picture

(사진) 찍어줘 : take a picture for me <— non-honorifix expression

(사진) 찍어주실래요 : take a picture for me <— honorifix expression
<Question>
is it 찍으실래요 or 찍어실래요

<My answer>
@캬라멜 함께 (사진) 찍어실래요 is right
That means "Shall we take a picture together"
함께 사진 찍어요 : Let’s take a picture together
(사진) 찍을래 : I want to take a picture(사진) 찍어줘 : take a picture for me <— non-honorifix expression(사진) 찍어주실래요 : take a picture for me <— honorifix expression
<Question>
함께 사진 찍어실래요 ..shall  we  take  picture together?
How  about  ?can  I   take  a  picture of  you  (연예인에게)한국어로 어떻게 말하나요. ..?  너의 사진을 찍을 수 있을까요?  
맞아요?
<My answer>

1) To the young : (죄송하지만) 사진 찍어도 돼요2) To the elder : (죄송하지만) 사진(을) 찍어도 괜챦을까요?3) To the very elder : (죄송하지만) 사진(을) 찍어도 무례가 아니겠죠?