tsure on "Connecting to on-line MySQL database"

When you say "SQL String" you mean SQL Queries then WordPress will take care of that if you are using WordPress and it's installed database.

However if you are using a different database (eg other than i1234_wp1) then it is your job to configure WordPress to connect to that database and write your own queries. See the following link for more information on using different DB tables:

https://wordpress.org/support/topic/pros-and-cons-of-adding-tables-to-the-wp-db?replies=8#post-1201613

~Tanveer