To avoid fee fees. My advice is you can make a purchase in the form of a voucher. Many sell bitcoin vouchers. And the fee is not too expensive. Please try it.

What about cheapest fee platform to use?

It depends on your location and a platform that you're going to use. You can also use coinbase pro where you can withdraw digital assets for free. There are also helpful techniques on the internet that you could use. Just be eager to do some research and try to look for a cheaper payment method.

Can we buy cheapest via online??

I would suggest you buying by indodax because they offering us when we buy/sell and we as a customer making a marker for the coins indodax will not include the fee trading for the marker ( We got 0% fee for marker order ).

This is the best option for you if you are looking to avoid fee then you have to do a peer to peer buying, because the sender will bear the burdens of sending fees, if not on the exchange the miner decide the fee you pay because the exchange will definitely take the fee from you purchased amount before sending your balance to you.

If you want to exchange from any exchange site it depends over which exchange site you use for exchange your cryptocurrency, peer to peer is best I think for decreasing transactions fee! so you can try for peer to peer exchange with local bitcoin holders.

Don't think about it where to bu bitcoin with the least amount of fee, think about it where to buy bitcoin with the most secure way, people really try so hard saving up a dollar or too and they end up being scammed because of it so they go on these shady websites and the get scammed and than they start complaining about it, my advice for you don't risk your money and go around looking for a way to buy with less fee, just go and buy from coinbase or any other trusted websites, they difference in the fees is not that high to be taken in consideration.

all exchange can big fee to taker and maker, so you have to put your order without past sell be taker.  or you mean fee for withdraw into own wallet?, like binance have big fee to WD, depends what exchange?, very popular exchange can be have big fee for that.

when you use third party platform like selly, shoppy, or anything flatform, can take fee from you

The best way to eliminate additional fee is possible finding a trader who wish to sell bitcoin directly in exchange of fiat. This is possible through our forum's exchange services section. You could find the trader and make the direct trade, and for trust it is a must to have an escrow. If there is no escrow then it's purely the high risk involved trade in my view.