The key thing you’re missing is that \$DC \times Check\$ gives you your progress, in silver, for each week. So after 1 week, your 16 check against a DC 12 makes 192 sp worth of progress on the arrows. Since 20 arrows cost 1 gp—that is, 10 sp—you easily complete them in that week.
If you want to measure progress by the day, you have to do things in terms of the item’s silver multiplied by the number of days in a week, instead: \$DC \times Check\$ becomes your progress in (typically) sevenths of silver. Thus, one day makes 192 worth of progress—greater than the 70 that you get multiplying 10 sp by 7 days in a week. So you can actually complete 20 arrows in one day.
It’s well worth asking your GM if you can work on more than 20 arrows in a day. Usually, you can only work on one item in a day, no matter how quickly you finish it, but since ammunition comes in bundles, it makes sense that you could do more. At 1 gp for 20, that’s 0.5 sp each—multiply by 7 for a target of 3.5. 192 worth of progress each day implies you can make 54 arrows in a day (a target of 189).
As for the longbow, assuming you aren’t trying for a masterwork or composite longbow, that’s 75 gp—750 sp. Since this is a more expensive item, it is best to measure progress by the week. So you make 192 sp worth of progress per week. Thus after week 1, you have 558 sp worth of longbow left to make. Another week, another 192 sp, now you have 366 sp worth left. A third week gets it down to 174 sp. So on the fourth week, your 192 sp of progress is enough to finish off the longbow.
So in the end, you can make a longbow in 4 weeks, and you can easily make 20 arrows a day—if allowed, you can actually make 54 a day.
Please note that once you get into expensive materials, masterwork or composite items, and so on, mundane crafting gets prohibitively time-consuming. A wyroot composite (+5) longbow costs 4600 gp—a staggering 46,000 sp. Even with rather high checks, and taking advantage of the rule that lets you increase the DC by 10 in order to progress faster—for example say you manage a DC 32 check perfectly, for 1024 sp worth of progress per week, that’s 45 weeks to complete. An adamantine full-plate costs much more, and so takes far longer.