Can an fir be withdrawn with an affidavit and dsp approval?

FIR  can be  canceled  or  quashed  only  by court  based on merits 

An apology  letter  and police  officer  recommendation  will not  work .

It is  better to file  a petition  to quash the  FIR based on the  letter, if you have  a copy luckily 

The police cannot withdraw the FIR.

They can file a closure report before court if there's a compromise between parties but again if the offences are non compoundable then the police may not do that also without proper investigation report to file closure report.

Your lawyer seems not advising properly.

You may change the lawyer to be safe about protecting your interests.

FIR cannot be cancelled or withdrawan by an affidavit from complainant and approval by DSP.

OPTION 1:  The Investigating officer may complete the investigation with report that there are no evidence to the complaint which report, the final report, has to be filed with the magistrate and the magistrate alone will close the FIR.

OPTION 2: However if investigation are completed. and charge sheet has been filed. then FIR can be quashed only by orders of High Court.

Yes, you need to wait till the Police completes the invetigation and files report before the Court.

Once  FIR is registered, it cannot be withdrawn or cancelled  by police, FIR can only be quashed by H.C under sec 482 Cr.P.C or under sec 528 of BNSS, police can submit FR if on basis of investigation. 

A FIR cannot be withdrawn solely on the advice of a District Superintendent of Police (DSP). The decision to withdraw an FIR, even if the investigation has revealed no offense, ultimately rests with the Magistrate after the completion of the police investigation and the submission of the final report. 

While the DSP may provide advice and guidance to the investigating officer, the police cannot unilaterally withdraw an FIR, especially if the offense is serious or there is a strong case against the accused.

Your advocate seems to misguide you.

After completing the investigation, the police officer must submit a final report under Section 173(2) of the Code of Criminal Procedure (CrPC) to the Magistrate. 

This report includes the facts and conclusions drawn from the investigation. 

Dropping proceedings by the Magistrate is considered a cancellation of the FIR. This often happens when the investigating officer files reports such as FRT, FRMF, FRML, or FRNC. 

However, if a charge sheet is filed against the accused, there is no dropping of proceedings or presumed cancellation of the FIR. 

Your advocate seems not to be interested to take care of your interests in this case hence you may better terminate his services and engage a new lawyer

No is the reply to your question. 

Very well analysed, opined and advised by learned senior experts, which I endorse and appreciate their acumen.

Once FIR is registered it can be quashed by concerned High Court, none else. However, police (not to speak of a DSP even IG or Commissioner) has no power.

If you have settled the case, file a petition for mututal consent divorce enclosing settlement / compromise deed, which should include that alimony shall be paid in 3 equal installments in the Court through DD viz; on first motion (recording statement of both parties) second installment at the time of recording statement of parties in their second motion and third and last installment at the time of quashig of FIR.