T1-T2-T3 are connected physically on the air-side transit zone. Security checks are at the gate for T1-3
T4 is not phyiscally connected to T1-2-3 (there's a airside shuttle bus) and T4 has a centralized security
once you get off plane at T3, you'll be in the transit zone.
don't need to go through immigration/customs, just walk (or take airtrain) towards T1. go through security at the gate and you're done
if everything is on time, it'll be a breeze.
min connect time is 1 hour. on separate tickets, i personally would want more time (and spending time in Changi isn't bad)
map:
Changi Airport - Welcome to Singapore Changi Airport