I am about to start a game where I am playing as an Adepta Sororita and as such I am going to use flame weapons until I get to play with Bolters. I have 3 questions that do not seem to be covered in the PHB.

Do I suffer a penalty for using a Flamer (Basic) one handed since there is no BS test?

Do I suffer a penalty for using two Hand Flamers with the TWW talent since there is no BS test?

Could I use the Flamer (Basic) in one hand and a Hand Flamer in the other with TWW and still have both attacks as part of a half action?

I will be going down the TWW path anyways for dual Bolter use later on (if my acolyte survives that long without bloody explosions) but I would like to clear this up before I try anything that could cause in game time to stall out while we all look for an answer.

It wasn't officially stated in DH books, but I remember that in one of the other lines (Black Crusade?) it was explained: in case of flame weapon penalty to BS test transforms to the bonus to enemy's Agility test.

Could I use the Flamer (Basic) in one hand and a Hand Flamer in the other with TWW and still have both attacks as part of a half action?

"If you have the Two Weapon Wielder talent you can hold two weapons, one in each hand, and can make a single attack with each. This is a Full Action , and both attack rolls suffer a –20 penalty (your off-hand weapon does not suffer the normal –20 off-hand penalty on top of this). If you do not have the Two Weapon Wielder talent and you wield two weapons at the same time, you can use a Full Action to make a single attack with each weapon. However, you suffer a –20 to the attack roll with the weapon in your dominant hand and –40 with the weapon in your off hand." DH Errata, p.11

I suggest you to read p.11-12 of the Errata for understanding of Two-weapon attacks.