I am writing to

There are many variations as to how this could be written. This is my version:

I am writing to seek permission for extended residence at the college during the D2 period. As you are aware, the D1 period does not extend to the start of the new term, so that I will have to check out. Law students who have applied for D2 do not; and hence, my request for special permission to apply for D2. (((or are you asking specifically for "residency" - I don't know what D2 entails.)))

My difficulty is that my house is now being invaded by insects, owing to the construction work nearby, and is constantly beset by mosquitos. Even a brief visit back there occasions extensive wheals on my body.

I do sincerely hope you can extend the requested permission, and trust I will hear from you soon.

(Note the spelling of 'wheal' )

Oh, and I think it only fair to you and other forum members who might peruse this, and any other contribution I make to this forum, that Setanta considers:
"Bazza's English is piss-poor. I advise you to ignore anything Bazza says on the subject….If you (Bazza6) claim to be a native speaker of English, then i (sic) would not only say that your English is piss-poor, i'd (sic) say you were lying."

I noted it principally because it's wrong.

But also because "weal" is not the correct word to use here. You don't get a weal from an insect bite, but from whip lash or similar cause of injury.

The question is, my dictionary gives the same definition for "wheal" and "weal":

wheal [hwi:l]
n.
a raised mark on the skin (as produced by the blow of a whip); characteristic of many allergic reactions

weal [wiːl]
n.
a raised mark on the skin (as produced by the blow of a whip); characteristic of many allergic reactions

Plus, the word "body" sounds dead. Is there any other word with the same meaning to replace it?

the encompassing structure

Eh? I wonder whether English is your native tongue.

McTag is right.
I will not adopt the definition of the dictionary.

wheal :
Medicine : an area of the skin which is temporarily raised, typically reddened, and usually accompanied by itching.

That pertains to ANY insect bite.

See this, you'd be screwed:

Etymology of weal
early 19th century: variant of wale, influenced by obsolete wheal 'suppurate'
Meaning of weal
noun
1. the mark of a stripe. see wale.
2. an area of the skin which is temporarily raised, typically reddened, and usually accompanied by itching.

Link:
http://www.findmewords.com/definition-of-weal.html

Bazz, you can take my advice or not, it's freely given without any obligation.
But you're proving Setanta right, sadly.