Are butt implants safe?

Yes and No. Butt implants are safe but have a much higher complication rate than breast implants. Choose your surgeon wisely. Ask to speak to previous patients. Check their board certification and don't go with someone with american board of cosmetic surgery. It's not a recognized board in the United States.
Yes, however. Any surgical procedure carries a degree of risk, but butt implants typically have more complications than the alternative fat grafting procedure used to augment buttocks. The Brazilian Butt Lift (which uses the patients own fat) is, in my opinion, the better option in most cases. Be sure to speak with board certified plastic surgeons who have extensive experience with gluteal fat transfers.
Yes. Buttock augmentation surgery is safe. However, the risk of infection is higher than other cosmetic surgeries, due to the location.