Hi Slimfish,
Your schematic looks good.
R21 was added by Seeedstudio in Rev 1.3 of the PCB. It looks like a current limiting device, but its real function is a fuse. Since there is no charging IC, if the battery & diode shorts, the power dissipation in the 1 Ohm resistor is nearly 100 x the rating of this 402 device, so it will open.
You are right, this resistor is not necessary with a functioning charge control IC.
The 10 K resistor I added is not necessary, since R25 and R26 will discharge C16 and turn on the FET.
I never looked at the charge current with the IC. Since you brought it up, and other postings have mentioned issues charging from USB ports, the charging current is way too high. Since we don’t have access to the battery manufacturer’s specifications, and the circuit does not have thermal sensing of the battery, fast charging at 1x the battery Capacity © is another way to shorten the life of the battery.
Normally the standard charge rate for these batteries is C/10, which in this case would be 0.5 Ah/10= 50 mA per hour. This means a fully discharged battery would take 10 hours to charge. Without more information about the battery, I suggest a compromise of 100 mA charge current, yielding a full charge in 5 hours. This would require R27 = 10,000 (10k) Ohms.
Connecting the “charge state” pin to the uC should be straight-forward. The IC has a version with a 3 state output indicating “charging” and “charging finished” (MCP73831, same cost).
There are excellent Battery & Power Management ICs from many vendors which could be used, but they cost significantly more (>2-5x).
NOTE to all in this post: two of the outstanding features of the DSO Nano which attracted me are the price and size. While firmware features and PCB traces have no production costs, hardware parts do. If portable full featured, 2 channel DS scope is what you want, they are available for $500 - $600 (i.e. Hantek and Owon). Many of the choices made by SeeedStudio is this design were obviously made with getting the most performance for the least price. So while we can suggest improvements, try to keep in mind these factors.
Shazam