For some reason I couldn't download the sgf (maybe just me!) so I've made some points below
1-4 - try not to labour too much over these, pretty much any move in the corner is "right" just do what feels good for you
- not necessarily the only move, tenuki and D4 are possible. Although D4 can become very complex
- both tigers mouth and sold connection are fine! there are subtle differences but generally not until later in the game
- A bit far/high, usually at C/, C10 or D10
- I agree with leela here! you are ahead after black takes the 3-3, your stones are all working nicely together :B27: - black's cut is overly aggressive inside your sphere of influence, you dealt with it well
- again I agree with Leela, pressing at A is much better
- after K4 there looks to be something quite tesuji-like at M3, a shape worth knowing
- empty triangle isn't quite right but cloe. A better move is at S16 although I think this group has trouble living whatever gets played here 
- you're right, A is much better, the black group looks pretty dead after this
- Unfortunately J18 is urgent
- well done spotting the ko, just a shame not in the game 
- this atari isn't good, connect at M2 and leave a peep at J3 or a hane at K1 for good endgame laterI don't believe your assertion that you're not 13k! At this level there's a high variability between games, so you might play like a 17k one day and a 10k the next. Without the mistake with the dead group at the top you really weren't doing badly at all!
I think pointers to take away are:
- Be more aware of your weak groups and cutting points, this is something I have a problem with too!
-think carefully about direction of play the proverb "play away from strength" is one of the most useful in my eyes
I hope that all makes sense!
