After my appendectomy, I started getting loose poops after meals. Are they related?

Likely. Early after surgery, bowel function irregularity is common. Loose bowels and constipation can occur. Sometimes antibiotics after surgery can cause diarrhea, and even can cause intestinal infection (c. Diff.). Trying probiotics supplements or yogurt may help. If you have persistent diarrhea that does not improve, see your surgeon.
Depends. This could be normal after any bowel surgery but be aware that it can be a serious superinfection and you may need special antibiotics. Eat yogurt and if this persists or worsens pass a few days or if fever then call your doctor.