I have done this a couple of times, and i think its depending on each patients bite, if you have a regular bite, or overbite , or overject, but there si always a solution, more than be filed down there are some ways to make them aesthetically nice, searching for that solution that you are...
No, this is not true , there are great proceedures that can be done with dentures, one of them can be snapindentures, this is a conbined proceedure with implants and dentures, they are affordable , and you can get great results , you should look at dental tourism , and see all the great options...
The best option for you is a dental implant for each missing tooth. The approximate cost for each Dental implant along with crown is USD 500 at our center.