RE: First Time Planing!
Congratulations on getting that Carve 145 planing! Good stuff, huh?
I would disagree pretty strongly with your "instructor" on the mast foot placement.
Putting the mast foot all the way up near the front of the mast slot, with very small sails (for the volume and width of your board) would seem to just about kill any possibility of planing with that board (Carve 145).
At 170 lbs. (77 Kg.) you aren't a really big sailor, and unless you are staying up by the mast foot way too long and your instructor has placed the mast foot that far forward for another reason, I would think the board would never get the nose high enough to plane off either freely (nose too low and planing surfaces at the back of the board not inclined correctly) or very early.
With such tiny rigs (5.0/6.5 m2) you are really well below the "sweet spot for the Carve 145 (sweet spot is in the 7.5-8.5 m2 range for light and moderate windspeeds).
So, move the mast foot back at least to the center (and probably as far as you can with your 5.0 m2 rig) and see if you don't get planing alot earlier and faster/more fleely.
As far as your 2nd "issue" here (board rounding up and wanting to go upwind all the time) that's a common problem for those sailors at your stage/skill level.
You are tipping the board upwind somehow.
Are you putting weight on your front foot in the down (toward the water) direction?
Are you all the way back on the board and in the footstraps?
Are you using the inboard footstraps?
How far back on the board are you getting?
The Carve 145 almost "requires" that you get your front foot back to just ahead of the front footstraps in order to plane off freely.
If you are using the inboard FS positions, you aren't getting enough "leverage" to really steer the board at your weight.
So, to correct this issue, you need to carry your rig a bit more upright,
stand directly over the boards fore and aft centerline, and keep your weight centered there until the board begins to plane.
Wish I had a video of you trying to get going as it would tell us in a few frames which of the common intermediate transitional problems is at the root of your issue here.
Answer some of the questions above, and I'm sure we can help you through this issue and have you sailing across the wind on a beam reach (or a little below a beam reach so your board can gain speed and plane off more easily.
Then we'll work on the "next level" of going upwind (on the fin) which will give you a much better angle and significantly better speed upwind.
Hope this helps,