Buy a little development board and learn how to use the ESP8266. Either a NodeMCU or a WEMOS board. They have a USB to serial adapter on the board and a proper regulator.
The initial problem you encountered was most likely caused by insufficient power for the ESP8266. The power supply must be capable of supplying a minimum of 400mA. It needs to have close short wires to the Vcc and ground on the ESP module. It helps to also have a capacitor across Vcc and ground of the ESP module with short leads.
There are some horrible examples on the internet that show the ESP being powered from and Uno's 3.3v power connection. This will never be reliable if it does even work. There is not enough power.
The ESP8266 typically uses about 80mA. This is an average value. When transmitting the peak current is a lot hight. The worst case happens to be when the ESP starts after a reset. I then does an analog power calibration. (for the RF section) Expressif states this, plus the digital power requirements, will equal above 500mA.
The GPIO pins are not 5 volt compatible. A lot of internet examples show the ESP rx and tx lines connected to the rx and tx of a 5 volt Arduino board, without level converters. This is not acceptable. The RX line of the ESP8266 can be damaged.
Powering the ESP module with 5 volts can damage all or parts of the two chips on the module. (the CPU and the external Flash memory chip) Other sections may still work. That is likely what you are seeing.