no, that's not faith, by any definition of the word (religious, secular or etymological).

You _can_ have non-religious faith on _people or institutions_ (not necessarily religious, but faith isn't the same as _any set of arbitrary assumptions_ (which is your example). Basic assumptions (in particular those you have evidence for or don't require an internal justification to exist) aren't faith.

Most definitions of the word also require _commitment_ to something or someone, as part of the definition of faith - so someone who blindly trusts a specific car manufacturer and always buys that brand has faith in it, whereas someone who just expects their brakes to work does _not_ have "faith on the brakes".

Trusting someone's word over something trivial isn't faith, it's just trust.