Hello. I have a question about powering the esp8266 d1 mini module. Previously, in my projects, I did it like in example 1. That is, I connected the batteries to the stabilizer and then to pin 3.3v in d1 mini. But now I would like to connect the module like in example 2, that is, to pin 5v (without ams1117). And now the question is whether they connect a battery that is fully charged has 4.2v to pin 5v, whether d1 mini will work for the same length of time as through the stabilizer (ams1117) or maybe shorter .. or maybe it doesn't matter?
Neither solution is very efficient, it really doesn't matter.
maybe, but in my case there is probably nothing better because generally I try to install LEDs in small car models (1:24 scale) as lighting controlled by the D1 Mini module via a webserver.. and generally I have a limited amount of space.. I used old batteries from phones earlier, but currently I try to use 13350 batteries from used disposable e-cigarettes. of course, in e-cigarettes, apart from 13350 batteries, there are also Li-poly batteries which are also suitable. well, generally it is known that it will not work for long, but for demonstration purposes it is suitable
Example 2 should work much better. The 3.3V regulator on the D1 Mini is the ME6211, which has a very low dropout voltage - nominally 100mV at 1A, but it's really somewhat higher than that. But the AMS1117 has a nominal 1.2V dropout voltage, meaning that its regulation will be compromised below 4.5V. Since your battery is at most 4.2V, the AMS1117 really isn't appropriate for single-cell lithiums. The ME6211 is just a better regulator.
Of course if you have a clone of the D1 Mini, the regulator might not be an ME6211.
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If example 1 was OK then example 2 will also be OK. You are not going to damage anything or see any big difference.
Because I thought that if the battery is connected to the 5v pin, when the voltage in the battery drops to about 3.5v, the module will stop working, and if it is connected via a stabilizer and to the 3.3v pin, even if the battery has 3.5v, it would still work..
but if it doesn't matter because it will work the same way, then there is no point in me buying a stabilizer if it is unnecessary
Neither one is likely to work, at least not well or long. Use 2 in series, then an LDO or buck to drop the voltage to 5V
What is a stabilizer?
That isn't exactly true and the only real way to find out if there is a big difference is to do a bunch of testing measuring voltages and currents, blah, blah, blah... but like I said I don't think you will notice a big difference especially if it's just for demo purposes and you not trying to break some world records.
You mean you don't know?
Try reading the entire post from the beginning.
OP seems to be using the term synonymously with regulator but is expecting it to act more like a buck/boost converter.
The D1 Mini has a regulator built in. It does exactly what your external "stabilizer" does, but it performs better. It seems you do not understand what an AMS1117 is. It's just a voltage regulator, and it requires some headroom to work properly. At 3.5V, the AMS1117 would probably have cut out long before that.
There is absolutely no point in buying an AMS1117 regulator. Connect the battery to the 5V pin, and save your money.
I know, I was hoping to get him to use the correct word.
I agree here, person that is playing with li-ion batteries might make one minute research about 1117.
It's linear voltage regulator, not "stabilizer" or "step down".
and excuse me, because I use google translator:
stabilizer ( stabilizator)<---- Polish language
it's also called AMS1117
Explains a lot. 
Anyway, leave it on side like suggested above
Example 1 is no good because the ams1117 will drop too many volts.
Example 2 is good, this is how I power many of my D1 mini circuits.
However, you need to protect the 18650 otherwise it will be damaged by over-discharging. Once is it damaged, when you try to recharge it, it can get hot, explode or catch fire.
I use 1800mAh Li-po packs with my D1 mini circuits. These packs contain a protection circuit which cuts the power when the voltage gets low, so that over-discharging does not occur. These circuits last 10~12 weeks before a recharge is needed, because the D1 mini is in deep sleep for 15 minutes, then wakes, connects to WiFi, reads sensors, transmits the data to a server and goes back into deep sleep in around 10 seconds.
Usually, 18650 batteries do not contain protection circuits, but some do have them. If you do not know, your battery probably does not have protection. You can add a protection circuit between the battery and the D1 mini.
The best option is to replace the Wemos with an ESP32 board with Lipo battery and built-in charger. The Seeed XIAO ESP32C3 is such a board. Low power draw and single-core, like the ESP8266.
Leo..
generally, that I only use for demonstration, the power is turned off by the switch.. and I only turn it on when I want to show how it works. and generally I use one cell or battery from the phone.. but that now I want to use only Li-poly batteries and 13350 cells from e-cigarettes because that's all that will fit in a 1:24 scale model. However, when it comes to charging batteries, e.g. 13350, I use a TP4056 charger, but one guy recommended replacing the SMD resistor that is on the charger. because charging with this charger can damage the battery.. but there is more in this tutorial (so as not to write too much)
https://www.youtube.com/watch?v=qCFdlcmdSMs&t=923s
I've seen this Seeed XIAO ESP32C3 on YouTube a few times but it's more expensive than esp8266 d1 mini.
I was also thinking about ESP32 super mini but it seems to have a bad wifi range because the antenna placed there has a poor range.. maybe it's placed too close to the chip and it interferes with its operation (I don't know if it's true but someone said something about it)