Enabling desired date format for users

I don't want to force users to use only mm/dd/yyyy format on my website.

My case: User will be able to choose which date format he prefers on the website ( calendars, tables and so on):
12.30.2016
12/30/2016
Dec 30 2016
30 Dec 2016

I don't want to put any restrictions on date input format the user can ENTER ( regardless of whatever date format he will use for display). So any input will be valid
12302016
12.30.2016
12/30/2016
30Dec2016
30 Dec 2016
30 December 2016
30 Dec (automatically will place the current year)

Q 1:
Is it a good practice to do stuff like that ( I don't see any reasonable limitation to force the user to enter only specific date format.)

Q 2:
Is it a good idea to replace the date format to the user's set custom format after he moves to the next input? (e.g. Users enter "30122016" but when he moves to another field the date will be replaced with 30 Dec 2016)

The product is made only for US market