1 & 2. No.
You have written your answer to your questions in your post.
You have posted that;
--"However release from services of the Company will be subject to satisfactory handover of the responsibilities assigned to you."
You may submit your notice addressed to good offices of your appointing authority, MD/CEO, Company Secretary with a copy to Head-HR, and mention effective date of resignation/last day in office in your notice of resignation you may ask in writing what are handover of the responsibilities assigned to you and what satisfaction company wants from you.
--"My department works in short 3 days to 7 days projects and basically there is no kind of handover or ongoing project that i would be abandoning when I quit." So you may also write that there is no project assigned to you and nothing is pending to be done by you.
--You may write that routine may be assigned to you on day to day basis which can be completed within and up to your effective date of resignation/last day in office only. Company may ensure that exit formalities are completed well in advance and acknowledgment and acceptance of your notice of resignation is supplied to you at once, and acceptance of resignation , work experience/service certificate ,relieving letter, form 16,PF number, attested copies of PF withdrawal /transfer forms (as decided by you and as per forms submitted by you),PF accumulation reports for entire period of your employment, NOC/NDC, FNF statement, payment of your dues by bank DD only is supplied to you within and maximum on your last day in office. All communication, payments should be supplied to you by redg. post only. You may mention in writing that you are enclosing postage prepaid, self addressed envelope (as purchased from PO) for sending the redg. post to you. You may write that the notice pay as applicable may be adjusted in your FNF statement and tentative FNF statement may be supplied to you at once, and that it is affirmed that amounts if any payable shall be paid by a/c payee cheque favoring the company under proper acknowledgment on letterhead of the company under original seal and signature by hand of the competent employees of the company which has to be issued to you on the spot. You may avoid payment of notice pay till the notice pay is not computed in FNF statement to avoid double taxation. You may also go by the advice of your CA/Lawyer on this point.
You may supply regular reminders under proper acknowledgment.
On your last day in office you must tender your final resignation, under acknowledgment.
You may submit all communications under acknowledgment at reception/counter where all mail/dak of company is received and obtain acknowledgment on your company with seal and date, followed by email, redg. post.
You may print copies of all relevant communications and forward all relevant emails.
The line management is not sure of finding, training, and making the replacement functional by last day in office of exiting employee hence all the pressure. Moreover HR/Admin wants line management to own the responsibility of carrying on the work hence HR and line management colludes to adopt tactics.
Employee should not falter in written communications and upon building favorable records. Employee should remain amiable, cool, and apply rapport, goodwill, and exceptional levels of persuasion, persistence, reasoning, negotiation skills to resolve the matter in his favor. You may help the line management in finding/ training your replacement.
Valauable advice of learned experts/members is sought.