ESP8266-01S (AzDelivery) x Arduino nano (AzDelivery) not working

Question

I'm trying to work with my ESP8266 but it won't work. I followed this (https://www.youtube.com/watch?v=ZJnpgYlelEA) video but it won't work. I thought, that my power supply is too low, so i used a LD33CV to convert the 5V to 3.3V with the hope of higher current. I messured the current with 50mA using the 3.3V (from board and converted) and 60mA with 5V. I tried to use 5V without converting, but it's the same. When turning on, the ESP8266 Flashes for a millisecond and when uploading a program the LED pulses. After uploading, nothing happens. I have a spare ESP8266 laying aroung, which i tried, but it's all the same. I don't see anything in the Serial Moniter (tried low baud rates too) so i tried to work with the WifiAP Example:

/* Create a WiFi access point and provide a web server on it. */

#include <ESP8266WiFi.h>
#include <WiFiClient.h>
#include <ESP8266WebServer.h>

#ifndef APSSID
#define APSSID "ESPap"
#define APPSK  "thereisnospoon"
#endif

/* Set these to your desired credentials. */
const char *ssid = APSSID;
const char *password = APPSK;

ESP8266WebServer server(80);

/* Just a little test message.  Go to http://192.168.4.1 in a web browser
   connected to this access point to see it.
*/
void handleRoot() {
  server.send(200, "text/html", "<h1>You are connected</h1>");
}

void setup() {
  delay(1000);
  Serial.begin(115200);
  Serial.println();
  Serial.print("Configuring access point...");
  /* You can remove the password parameter if you want the AP to be open. */
  WiFi.softAP(ssid, password);

  IPAddress myIP = WiFi.softAPIP();
  Serial.print("AP IP address: ");
  Serial.println(myIP);
  server.on("/", handleRoot);
  server.begin();
  Serial.println("HTTP server started");
}

void loop() {
  server.handleClient();
}

No Serial Output, No Flashing, No Wifi showing up

Edit: After work, i came home and tried it again (without flashing). I just plugged the already flashed (yesterday) in and got a response. I think, that the ESP8266 needs to be manually resetted. After flashing it again, it didn't work anymore. I tried this code:

void setup() {
  Serial.begin(9600);
}
void loop() {
  delay(1000);
  Serial.println(1);
}

but nothing happends anymore. I put a switch between GND and RST and i pressed it, even holding down doesn't help. Replugging the ESP doesbn't help either. The only thing that happens, is a response of some characters (random) in the Serial when resetting. I tried to print "test" before, still the same

Edit 2: I slightly got it to work. I uploaded the sketch above and it worked after replugging the USB cable a couple times. To flash the ESP8266 i used this method from https://tttapa.github.io/ESP8266/Chap06%20-%20Uploading.html:

1. press and hold the reset button
2. press and hold the program button
3. release the reset button, the ESP 
4. will boot in program mode
5. release the program button
6. upload the sketch

After pressing the reset button, it prints a, what seems to be, random string and it doesn't work anymore. After that I have to replug the USB cable for a bit until it works again. But even without receiving a serial output, I can see on the Arduino nano, that it is getting responses because of the flashing Rx (or TX, I don't know rn I'm at work) LED.