Is seems strange to add a -t at the end of "tysk"
Not at all. 'Ett företag' is a neuter noun, so all adjectives used to describe it (unless they're plural) take -t at the end.
Have you been reading the tips and notes before each lesson?
In Swedish, don't they make the first latter of the counrty's name with the capital latters ?
Yes, but this isn't the name of the country - it's the adjective. Swedish doesn't capitalise that.