There are multiple types of key signatures in Dorico Pro, which can all be input, moved, and deleted in the same ways.
Major and minor key signatures
The key signature for a major key appears the same as the key signature for its relative minor, and vice versa. For example, B♭ major has two flats in its key signature. This is the same number of flats as for G minor, which is the relative minor key to B♭ major. The difference is that music in G minor usually has sharpened Fs, as the seventh degree of the scale is raised in minor keys. Therefore, if you input an F♯/G♭ after a G minor key signature, Dorico Pro prefers to spell it as F♯ in most cases, in order to follow the convention of harmonic minor keys.
Open key signature
Although open, or atonal, key signatures appear the same as C major or A minor key signatures because none shows any accidentals, open key signatures behave differently.
In an open key signature, the spelling of accidentals is based on the current direction of the music. If the music is rising, sharps are preferred, whereas if the music is falling, flats are preferred. There is no hierarchy of pitches in an open key signature, so the same pitch might be spelled differently each time it appears depending on its context, even within a few bars.
In a C major or A minor key signature, accidentals are spelled based on the context of the major or minor tonality implied. For example, in C major, sharps in general are preferred, whether the music is going up or going down. Similarly, in A minor, G♯ in particular is preferred, whether the music is going up or going down, as G♯ is the leading note in A minor.
No key signature
Some instruments are accustomed to seeing no key signatures in their parts, no matter the overall key of the piece. These instruments include timpani, percussion, horn, trumpet, and sometimes the harp. If you have added the No key sig version of these instruments, then no key signature is shown in their parts, even if they are a transposing instrument, such as horn or trumpet.
Any pitch can be input into these instruments, and they show accidentals if needed.