Converting pattern from flat to round

I am still a bit of a beginner and I am trying to knit a hat. I already converted most of the pattern from flat to round and I know that everything is opposite and in backwards order but I’m just unsure about a few points.

"p into back and then front of next st (increase made)"
Does that mean I K into the front and then back? Or would it still be K into back and then front?

"Row 1: *k6, (p1, k1 tbl) twice, p1; rep from * across."
Would I do the P1 into the back loop still?

"3/3 LC (3 over 3 left cross) Sl 3 sts to cable needle and hold in front of work, k3, then k3 from cable needle."
This is the cable part of the pattern so would it still be kept as K3 or would I have to convert it to P3?

"p into back and then front of next st (increase made)"
Does that mean I K into the front and then back? Or would it still be K into back and then front?

You can knit into the front and back. For purls it’s just easier to do back/front for an increase.

"Row 1: *k6, (p1, k1 tbl) twice, p1; rep from * across."
Would I do the P1 into the back loop still?

I’d say go through the back loop as well.

"3/3 LC (3 over 3 left cross) Sl 3 sts to cable needle and hold in front of work, k3, then k3 from cable needle."
This is the cable part of the pattern so would it still be kept as K3 or would I have to convert it to P3?

The cable cross would be on the right side of the work either way, so keep them as knits.

Thank you so much! I’ve asked so many people but you’re the first one to give me straight answers!

As long as you do it the same way every time, it won’t matter. Holding it in front will give you a left-leaning cable; holding it in back will give you a right-leaning cable.