Regarding apply of TAN

If TDS not deductible, no need to apply for TAN.

You can give Salary Certificate to your employees, when no TDS deducted (deductible) from salary.

You cannot generate form 16, when no tax paid or no TDS return filed.

You can give only salary certificate for 12 months, so that employee can provide it as proof of salary received in particular FY.

Yes. Based on the certificate, an assessee can file ITR. (provided the gross salary is below Basic Exemption limit)

But if Gross salary is above BEL, the employee has to file TDS return (even if net taxable amount be below maximum amount not chargeable to tax)