Oin expends 1 AP to move her BMR (20') in the first phase, expends 1 AP to move her BMR (20') again in the second phase, expends 1 AP to melee in the third phase and 1 AP to melee in the fourth phase; then attack at -50 for spending 2 AP. He couldn't have expend 1 AP to move in the third phase because he moved double is BMR (40'): 20' in the first and 20' in the second phase and he is limited to a jog pace.
That's fine exactly as you have it. This is using AP for movement, and then attacking with the remaining AP.
Goin expends 1 AP to melee and move at a jog pace 10' (half his BMR of 20') in the first phase, expends 1 AP to melee and move at a jog pace 10' (half his BMR of 20') in the second phase, expends 1 AP to melee and move at a jog pace 10' (half his BMR of 20') in the third phase, expends 1 AP to melee and move at a jog pace 10' (half his BMR of 20') in the fourth phase; then attack at -50 for the jog pace.
Also correct. This is moving while acting, incurring a pace penalty instead of an AP cost.
It's useful to note that there is the same amount of movement in each case (40' total) and the same penalty (-50). So in many cases it doesn't matter which way you choose to handle this, by design they work out the same.
However, Goin can apply any Footwork skill he may have to offset the -50 pace penalty. Oin cannot, because Footwork doesn't offset the penalty for making a 2 AP attack. So if you have Footwork, you may be better off moving while attacking.
That might seem a little odd but consider this alternative scenario:
Oin stands in place and makes a 2 AP attack during phases 1 and 2. Then in phase 3 he spends 1 AP to move 20', and in phase 4 he spends his last AP to move another 20'. In this case, although he's doing the same combination of things as in your example, tactically it's an important difference that he's running away after attacking. It would not make sense to allow Footwork to help you attack in place and then run away afterwards.