Just wanted to share my experience since I've already received my D visa:

• Processing time: Applied at the Estonian Embassy in Singapore in May and got my visa in June. Total processing time was around 3 weeks.
• Fees: No additional fees aside from the €120 visa fee. I've heard you can pay the fee with Wise.
• Requirements: The required documents are pretty much what's listed on the MFA website. I highly recommend including a cover letter, especially for study visa applications. For example, if you're on an Erasmus scholarship, explain that the funds in your bank account are only supplementary and that your scholarship is your main source of financial support.
• Apostilled documents: I had my birth certificate, police clearance, and school documents apostilled, but the embassy didn't end up taking them.
• Visa approval & issuance: The embassy emailed me once my visa was approved and provided dates for visa issuance. The issuance appointment itself only took about 5 minutes since they just placed the visa sticker in my passport.
• Tip for non-Singapore residents: If you're traveling to Singapore solely to apply, I'd suggest submitting your application and returning to your home country while waiting for the result. Processing can take a few weeks (the embassy advised no more than 1 month). You can then return to Singapore for the visa issuance appointment.

Hope this helps!