Dean, College of ****(or) Chairman, Department of **** Sorry, but, Sir, I've been asked to directly address the principal. Will it be wrong to do so? -- Universities in my country do not have principals; principals are heads of primary and secondary schools.
Dear Dr [Dean's/Chairman's surname]: I don't know his name. Will it be wrong to say "Dear Sir"?-- Only if you cannot manage to learn his/her name.
I have completed my intermediation (diploma? certificate?) [thank you again, Sir. Yes, it's a certificate. Can I say "H.S.C."?] -- it would be better to spell it out in full: High School Certificate (?)
in pre-engineering, and would like to pursue a BE (Telecommunications) degree at ABC University. [Do
I have to use the university name here. I am confused a bit. When I
have already mentioned it above in the address section, do I again need
to mention it here?]-- Yes, use it again. 'Highly estimable' is simply fawning.
I have always been interested in telecommunications, and more recently I have narrowed my goal to becoming a telecommunications engineer. Enclosed/attached are my educational records. [I've already provided them with all the necesarry documents and records.] -- Then mention that fact here.
Since my family is unable to bear the full cost of tuition, could you advise me of any financial assistance available? [They
have already given me a concession of 50% with the grace of God, but
they have still asked me to write an application letter for it as a red
tape. I know for a fact that bluntly mentioning the desired concession
is rude. Therefore, can I say "Since my family is unable to bear the
full cost of tuition, could you please offer me some financial
concession?"] -- 'Concession' is not a word I am familiar with in this context, but yes, use your sentence if it has been pre-arranged.
Sincerely yours, [As I have told above, I don't know his name. Do I still need to use "sincerely yours", or should I use "faithfully yours" now?]-- Yes, to be safe, use 'Faithfully yours', though few are aware of this fine point nowadays.