Can babies have nightmares at 2 or 3 months old?

Not in the true sense. At that age, the memory and imagination a nightmare requires simply haven't developed yet. Crying at this stage is almost always hunger, gas, or a startle reflex.

At what age do real nightmares start?

Most experts place the earliest realistic age around 18 months to 2 years, with nightmares becoming more common between ages 3 and 5 as imagination and memory develop further.

Do 2-month-old babies dream?

If they do, it's more likely simple sensations than an actual dream scene. A 2-month-old's brain hasn't developed the memory and imagination needed for narrative dreaming yet, so movements and expressions during REM sleep at this age reflect brain development, not dream content.