The power is a one way street. It will not output anything to the battery. You will need to connect a charger circuit in parallel to the Lipo battery. I assume there is some charger breakout boards available for low cost. I'm not totally familiar with the Nano circuit, but I guess you have 5V power from the USB available on the bard. So you can charge with the USB while its plugged in, but you need to connect the charger circuit to that 5V line. FYI, should charge the battery at half the mAh rating. So if its a 1000mAh battery, charge it at 500mA. Charging Lipo cells is very strict. Must be done at the correct voltage and current, or it can be dangerous or damage the battery.
If you have a good quality lipo cell with the safety PCB, it will be pretty hard to get into trouble with it. It won't allow you to input 5V, it will just turn off. Usually the max allowed is 4.25 +/- 0.05V. But I think most of them will allow a charging current that is beyond the safe limit, so be careful of that.
Also, the Nano cannot supply enough current at 3.3V to run the wifi module. It will probably not be able to connect to your router. The 5V signals from the Nano may damage the WiFi module, it is a 3.3V device. Other pins on the WiFi module also need to be connected to 3.3V.
Don't use Nano+WiFi module for this project. Use a Wemos mini. You can get a battery shield for the mini which will safely charge your battery when connected to usb.
The Vin pin on the Nano is the input to the voltage regulator, which is a 5V regulator with a dropout rating of 1V. That means it needs to have at least 6V on Vin to provide a proper regulated 5V output. But with USB not connected, your battery will supply at most 4.2V to Vin. So that's not going to work.
LIPO charging has to follow a specific pattern - constant current, then constant voltage, then shutdown at completion - to avoid really dangerous things like explosions. You can't just leave it connected to a power source.
I think the Wemos D1 Mini with the battery shield is a great idea for this so long as your pressure sensor will operate at 3.3V.
The DPS310 sensor should be 3.3V compatible, but post a link to the board you want to use before you buy it.
This DPS310 sensor board looks like it might be compatible with Wemos, but I do not think it is, so do not be fooled by its appearance.
It is quite an expensive sensor. Why did you choose it? What is the application? There may be less expensive alternatives, which might even be available as a Wemos shield.
I'm trying to make a rechargeable health band/watch which is targeted for sick elderly's whom stay alone at home.
The Plan:
to sense the temperature of the elderly, in which the temperature's will be sent through Blynk IoT, so that their love ones can see their temperature from work or from school.
to sense sudden drops with the DPS310 as that elderly's are commonly very frail and prone to falling or collapsing.
PaulRB:
The DPS310 sensor should be 3.3V compatible, but post a link to the board you want to use before you buy it.
This DPS310 sensor board looks like it might be compatible with Wemos, but I do not think it is, so do not be fooled by its appearance.
It is quite an expensive sensor. Why did you choose it? What is the application? There may be less expensive alternatives, which might even be available as a Wemos shield.
So you want to sense temperature and sudden movement? The sensor you mentioned is an air pressure sensor. It probably can sense temperature and sudden drops, but I don't think that was what it was designed for. I would suggest an accelerometer sensor. These can sense sudden movements and orientation, which might be useful.
Sensing a patient's body temperature is not easy. Or did you want to sense room temperature?
That is an ambitious project for a first project. But entirely doable. You will learn a lot doing this project.
I agree with Paul that a Wemos D1 Mini plus battery shield and an accelerometer are a better choice because the Wemos already has WiFi and it's a smaller footprint than the Mini plus ESP8266 board. (The Wemos can be programmed using the Arduino IDE).
A DS18B20 temperature sensor against the skin would give you a relative temperature. (Skin temperature is always lower than the body temperature).
WiFi is very greedy in energy : one connection can take several seconds with more than 100mA current. So battery powered wifi needs either "big" accus either short and rare connections...