First thing is that the most reasonable way of adding extra input fields to a post or page is via Custom Meta Boxes:
This topic is quite enormous so if you're confident with a bit more advanced programming and quite a lot of reading then go ahead - this would only improve your knowledge.
If your not confident with that then use ACF - I've been using this plugin for quite some time already and it's one of the best plugins out there (yet still it involves some programming on the Front End).
Anyway please remember about the data validation http://codex.wordpress.org/Data_Validation whenever adding custom user input (even if it's for your own sake - that's a good practice as well)
Likewise to output a properly formatted content filtered via wp editor please do the following:
echo apply_filters( 'the_content', $variable_name );
Where '$variable_name' would be the name of a variable which had the contents stored.
This solution would run a lot of different filters, outputting the properly formatted text.
Hopefully I haven't discouraged you. It is a good practice to avoid filtering the data as you did above, whenever there's a semi-automatic solution (like the MetaBoxes API).