what is the name of the drive-in hamburger joint featured in the first episode. i believe it burned down much later in the series

It was called Arnold's! Hello! It was burnt then they rebuilt it, it was there all 11 seasons

i read somewhere that in the first episode of happy days,the drive-in had a sign which read 'arthurs'.

Yes, you are correct Angelina.

I've always wondered if there was a place somewhere in L.A. area that inspired the restaurant. Was there really a place called "Arnolds" or was there a place that Garry Marshall was motivated by?

It was probably inspired from Mel's Diner in American Graffiti.