Can I restore an SQL 2016 database mdf at an SQL 2014 Sp1 instance? I have a database file .mdf created in SQL server 2016. I am planning to move at a new web hosting provider who supports 2014sp1 version. Should I proceed or this is out of specs? Can I restore an 2016 version at a 2014 one?
No You cannot. You have to bcp out data and bulk inert into 2014 or you can create sql 2014 schema + Data script and run the same on sql server 2014.

See my answer here : https://dba.stackexchange.com/a/55063/8783