I have a record player with a dual needle system... its old and i know i need a new needle for my LP's (because the one specified for LPs just slides right to the center of the album)

The needle for the 78 plays the records (the sound quality isnt amazing, im assuming its because its not the right needle). My question is:

Is it safe to use the 78 needle on my 33's and 45's?
also... by doing so would i have damaged the albums i did play with the 78 needle?