FIrst off, welcome back to Shadowrun and all that friendly stuff.
1. I read about the absolute minimum Drain for spells is 1, is this to mean that even if you roll enough, you still suffer 1 Drain?
The line you're talking about is on page 203 of SR4A, and the exact wording is that no "Drain Value" can be less than 1. A particularly stringent GM could argue that since your Drain Resistance Test reduces the Drain Value (SR4A, pg. 184), then the pg. 203 rule of minimum Drain Value is invoked. However, the section that the 203 rule is in is discussing how to read the format for spells, including calculated pre-soak drain. Therefore, the RAI is pretty clear that, no matter what, you have to roll a Resistance test.
2. The Adepts powers, are they always on? Or do you need to activate them to use them?
Some are always on, some are activated. Example: Attribute Boost is activated when you roll the dice and lasts twice the number of hits in Combat Rounds. Enhanced Perception, on the other hand, is always actively enhancing your Perception Tests (including Assensing, if available).