I have imported several items through trans-shipment services over the last 13 years. (I remember that my account with Borderlinx was opened in 2006.) I have imported a lot of used equipment, importing from eBay US, eBay UK, from sellers in Europe and US. This includes laptops, computer electronics, and audio gear.
I have also imported directly, without using a trans-shipment service, from the US (Amazon, eBay) and China (AliExpress).
My first trans-shipment service, Borderlinx, operates through DHL. They closed down some 2-3 years ago. My current trans-shipment service, Shopandship.com, operates through Aramex. Both have very similar operating procedures.
They both take a simple KYC document (PAN is enough) and a signed letter of authorization. They keep it in their records and never ask for it a second time.
Of late I've always paid 42% on the CIF value, as another FM has described. This is the current figure. Till a few years ago, it used to be more like 30-35%.
I've never tried under-invoicing. However, some AliExpress sellers do under-invoicing as their Standard Operating Procedure.
Heavy items often increase in final landed cost to me because of their weight. I remember my purchase of a pair of Fostex FF series 8" drivers. Their price on Madisound was $125 each. By the time they reached me, I had paid $250 each for them. (Each driver weighs about 4.5kg.) Even more extreme was my used Marantz 6.1ch AVR from the UK. I bought it from eBay used, for UKP 100. The seller shipped it to my Borderlinx UK address. This means I paid about INR 10,000 till that point. Then Borderlinx added India shipping, and India Customs added Customs Duty on top of it, and I paid a further INR 17,000. So my total landed cost became INR 27,000. The AVR weighed some 15kg or 18kg, I don't remember now.
It's wrong to say that Customs don't allow used goods to enter. All my used laptops and audio gear have come through without a single hitch. And both Borderlinx and Shopandship want copies of your original invoices for Customs clearance, and present these to Customs. And as you know, an eBay invoice includes the title of the listed item in bold, and most used items have the word "Used" in the title itself. I totally agree with other FMs that Customs inspectors are not fools. They know exactly what is coming in. They allow all my used items to come in, knowing exactly what each item is. Customs even has databases of model numbers and year of manufacture. So if they see a Canon EOS 5D Mark III today, they know it can't be new, because Canon switched to Mark IV several years ago. Therefore, my belief is that import of used goods for individual use is permitted. Import of used goods in larger quantity for re-sale screws the happiness of Indian manufacturers and is not permitted.
About courier companies: I don't want to touch FedEx with a 12-foot bargepole. Their customer service is worse than Reliance Telecom. I have had excellent experiences year after year with DHL, am getting decent experience with Aramex now, and I've recently had to deal with UPS since Parts Express ships through them. UPS seems a more sleepy company but is friendly and gets the job done.
You may wonder why I have imported so many items, and whether I'm in the business of doing this. I'm not. I do this because I am a DIY audio builder, and am constantly importing parts and drivers. Indian DIY sellers have terribly sleepy customer service -- they are often poorly stocked, don't have parts, don't know when they'll get fresh stock, or they'll take 2 weeks to just respond. (The only exception to this, consistently, has been DIYAudioParts of Hyderabad. Very good responses.) I always want to buy from Indian DIY audio suppliers to save the import headache but sometimes give up after their responses (or lack of response) and order from Parts Express and Madisound. For the first time, I even ordered a few crossover coils from Parts Express. None of the three Indian sellers could give me the simple coils in the values I needed. One of them said he'll check his stock, and it's been 3 weeks now. I'm still waiting. In the meantime I've even received the parts from Parts Express.
I've imported used audio gear for personal use for myself and one or two friends. They are far cheaper on eBay UK than buying new in India, and you get a wide variety to pick from. Buying used in India, from HFV members, is attractive too, but you don't get any choice or options; the range is very limited.
I also keep importing CDs from Amazon US. The CD market in India has practically dried up. Ditto, blank cassettes.
Borderlinx and Shopandship both charge me Rs.500 + taxes for handling and Customs clearance fees, over and above shipping charges. If you have problems with such fees, don't use them.
My experience with direct imports has been 100% success rates too. Packages may get delayed by over a month, so I only order direct post parcels for those items where delay is acceptable. In about half the cases, the postman has charged Customs on the package, and the rest have come through without Customs. A bit hard to predict which will get charged, which won't. I recently ordered a bench power supply from AliExpress which cost me USD 70 or so, and it came in by direct post with no Customs duty. Direct import through the post does not require any KYC.
Hope this helps.