Most cover songs are recorded in the wrong key. Not musically wrong - wrong for the specific human singing them. The original artist had their range, your singer has theirs, and the gap is usually a major second that everyone tries to power through until take nine, when somebody finally admits the bridge is not going to happen tonight.
Move the song. It's a ten-second job and nobody in the audience knows or cares what key the original was in.
Two tools, different jobs
Tutti gives you two ways to shift pitch, and people mix them up constantly.
Clip transpose works on a recorded clip. Select the clip, change its transpose value, done - the audio itself is re-pitched. Use this for the backing track you imported, the guitar part that's already down, the demo you're building around. It's per-clip, so you can drop the whole instrumental two semitones and leave the click track alone.
The Pitch Shifter device is an effect in the chain - drag it from Audio Effects onto a track and it shifts whatever passes through, live. Coarse range is ±24 semitones with a ±50 cent fine control. Because it's a device, it processes monitoring and playback in real time, which makes it the right tool when you want to hear the song in the new key while deciding, or shift an incoming signal without touching the clips.
For "we need this song in D instead of E": transpose the instrumental clips down two semitones and have the singer just sing. Don't pitch the vocal. A real performance in the right key beats a shifted performance in any key.
About the chipmunk
Everyone has heard what happens when you pitch a voice up more than a little: it stops sounding like a smaller person and starts sounding like a cartoon. That's formants - the resonant fingerprint of a throat and skull - getting dragged along with the pitch.
The Pitch Shifter has a formant switch for exactly this. With formant preservation on, the device moves the notes but keeps the vocal timbre where it was, so a +3 shift still sounds like the same singer on a better day. There's even a separate formant shift control if you want to mess with the character - shifting formants down a touch can make a thin vocal read slightly bigger. Small doses.
Instruments mostly don't need it. A guitar shifted with formants riding along just sounds like a differently-tuned guitar, which is what you want. Leave preservation off for instruments; that's the natural behavior.
Honest limits
One or two semitones in either direction, you can get away with almost anything. Past four, artifacts start creeping in on complex material no matter whose algorithm it is - ours included. If the gap between the original key and your singer is bigger than that, transpose the backing partway and ask the singer to meet it in the middle. That's what working vocalists do anyway.