Can you call a batch class from an Apex trigger? If yes, what are the precautions?

Yes, via Database.executeBatch(), but with care:

• Limits: only 5 batch jobs can be queued or active at once (extra jobs go to the Flex Queue, up to 100 holding). A trigger firing per 200-record chunk can flood the queue.
• Context: you cannot call executeBatch from a future method, and a batch can only start one batch, from its finish().
• Volume: one batch per trigger invocation, not per record. Collect Ids and launch once.
• Recursion: avoid the batch updating the same object and re-triggering infinite batches.
• Check System.isBatch() / System.isFuture() before enqueuing.

Consider Queueable Apex for lighter work.