Can someone translate and explain the language word/grammar?

[najmalidk]

Or why was (Y/n) asked what she wanted to eat in one panel and body-slammed in the next?

Basically, being asked what I wanted to eat and body-slammed after was what made me curious about this fanart.

I could understand most of the text with my basic Japanese knowledge, except for those I circled.

From what I can tell, here's what I assume those circled texts mean:
1) "You could tell me what you're doing with that phone, or I'll use my own method to find out,"
2) "that's the letter i sent you, isn't it? why is it in the trash?"
3) I'm writing a letter carefully while thinking about 夢主/ Y/n (too bad I can't tell what's happening in the image)

I'm pretty sure I just translated those three paragraphs too. Literally, that's why most of them don't make sense.
Can someone tells me what it actually translates to and where I made mistakes? I want an explanation because I want to learn too rather than enjoy a translation.

I really appreciate any help you can provide. (＾∇＾)ﾉ♪

 

[Toritoribe]

1)
代わりにやってあげる means "I'll do that instead of you."
Also, 調べたいこととか連絡したいことがあれば is a conditional "if you have~".

2)
Correct.

3)
This is not the man's (Sugimoto in Golden Kamuy?) words but a narrative part by the writer, as same as the two lines at the center of the page. It explains about his letter.

The key is the two lines I mentioned above. the manga is an example of the description about him.

 

[najmalidk]

1)
代わりにやってあげる means "I'll do that instead of you."
Also, 調べたいこととか連絡したいことがあれば is a conditional "if you have~".

2)
Correct.

3)
This is not the man's (Sugimoto in Golden Kamuy?) words but a narrative part by the writer, as same as the two lines at the center of the page. It explains about his letter.

The key is the two lines I mentioned above. the manga is an example of the description about him.

Alrighty! thanks for the answer, that cleared up a lot of things. at first i didn't think he meant an actual letter because we didn't actually see the letter in the comic at all and i'm pretty sure people hardly uses them these days. i thought he meant a text message or something. my mistake.

anyways, i'm still kinda confused about some stuff;
1) when he says "I'll do that instead of you," what would he do exactly? or is that not explicitly said in the text?
2) in the author's note does the text in the brackets mean "the picture is too bad to understand", therefore there was a picture attached to the letter...?

 

[Toritoribe]

1)
調べたいこと and 連絡したいこと are more likely "something you do~" rather than "what you do ~" there. Also, "the -masu stem of a verb + たい" doesn't mean "to be doing."
What is your translation of this conditional clause?

2)
添えてある modifies 絵. This ある is not a verb for existence "to be" or "there is~", but an auxiliary verb used in the expression "the -te form of a verb + ある." Have you learned this expression?

Isn't the man Sugimoto, by the way?

 

[najmalidk]

1)
調べたいこと and 連絡したいこと are more likely "something you do~" rather than "what you do ~" there. Also, "the -masu stem of a verb + たい" doesn't mean "to be doing."
What is your translation of this conditional clause?

2)
添えてある modifies 絵. This ある is not a verb for existence "to be" or "there is~", but an auxiliary verb used in the expression "the -te form of a verb + ある." Have you learned this expression?

Isn't the man Sugimoto, by the way?

yep it is sugimoto!! :>

and nah i havent learned the stuff you said _ ´ཀ`」 ∠):_

 

[Toritoribe]

"The -te form of a verb + ある" expresses that the action was done previously, and it is the present state resulting from the past action. It's hard to translate it other than "attached" in English, though.
What is your translation of 調べたいこととか連絡したいことがあれば?