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My question specicially is can a unit in a drop pod come in advance then fire a flamer? or is that specifically why flamers are 8 inches? also can sisters of silence ride any transports besides their rhino?

If it's anything like AoS, then no, since running (advancing in this case) is done as part of your movement, and deep striking would replace that.

No you cannot. There is a box on page 177 that addresses this.

Nope; 'running' is now tacked onto the normal movement phase so you have to plan way ahead.