Can I apply for a 30-day extension on my Thai visa immediately after arrival?

At most immigration offices you can apply when you have 30 days or less left. A few will allow you to apply when you have 45 days or less left (Chiang Mai, Bangkok, Phuket to name the bigger ones), and some will only let you apply when you have 7 days or less left (Pattaya, Koh Samui, Koh Phangnga)

30 days is going to be your safest bet unless you're in a place that limits you to 7 days. But nowhere will accept your application for an extension immediately upon your arrival.

Depends on which Immigration Office you will use. Each office has their own requirements.