I want to know if is possible to avoid some of the additional fees
Airport fee for example is easy – choose a location/company that does not charge it or a hire location away from an airport.
Energy/Environmental fees, where these are levied, are contractual obligations. If you want to avoid these try a different company.
In all cases, read the T&Cs.
and if is totally ok to decline the insurance offered by the rental agency, or buying cheap insurance elsewhere, or even use credit car insurance.
Yes. Insurances are generally of two types: Compulsory and Optional. The Compulsory insurance normally need not be purchased from the car hire company, provided suitable evidence of such cover is provided to them.
I want to know if there is a website where I can pay the car rental without surprises or added fees when picking up the car, just the price shown in the website.
Yes. For example I hired a car from Europcar via their website and the cost (before fees for my traffic infringements) was exactly as pre-paid. I will though admit that on an earlier occasion I was disappointed to be charged an exchange rate differential (but the cost of the differential was quite a lot less than the bank's foreign currency charge for settling the tiny amount). That was also Europcar, which I did not hire from on my next visit.
This is an image from Europcar.com, as for someone 26 or older living in the United States of America, hiring from O'Hare airport:
With and without insurance is clearly differentiated. I am guessing either O'Hare do not charge airport fees or at this location they are covered by "premium station surcharges" and hence built in to the displayed prices. Similarly I am only guessing that "VAT" covers any Sales Taxes. Either way it seems they should not show up on the final bill as extras but I can't confirm they do not.
For their Perth, Australia hires such details are more specific:
I was disappointed to read that the UK is little or no better. A Times article "Car hire extras still come as a surprise" of October 27, 2016 reporting on a Which? magazine study included:
Car hire companies are still smuggling hidden extras into the small print of contracts, leaving holidaymakers with higher than expected bills…
Nearly a third of the price of car hire extras, from additional drivers to dropping the car off at a different point, were not set out during the booking process online. This rose to 51 per cent of the charges added by Avis …
They also found that drivers were put under pressure to buy additional insurance they did not need or into hiring satnavs at extra cost when they picked up their vehicle …
Which? looked at 300 prices for car hire extras from seven of the biggest companies used by British holidaymakers to find that a third were either buried in the small print or not shown at all when booking online.
Since considering holidaymakers, it seems likely that at least some of the cars in the sample were driven in USA.