Is it acceptable to spell doughnut like donut and what about catsup like ketchup? Are these words changed due to the advertising world?

Ketchup is the English way of spelling 'catsup' . 'Catsup' is unknown in British English . Heinz Tomato [ 'Toe-Mah-toe' ] Ketchup is the best known and best- selling brand here.

There was a movement in the US in the 1920s and 30s towards orthographic reform, mostly directed at words containing -ough- . My mother, for example, wrote though as tho' throughout her life (alhtough, as you can see, I never picked up the habit.) As for catsup/ketchup, I suspect someone was trying to avoid trademark infringement.

Alan Moore

You've got it backwards. Ketchup is closer to the Malay word (kechap). Catsup (and first catchup) was an attempt at anglicanization, one that didn't catch on in England and either didn't catch on or has died out in most of the US.