Thanks Neoxelox for respond!
I just wanted to make an update. Almost all yesterday I’ve spend on forums and testing different solutions. I’ve understood very important thing - Cayenne & WiFi Shield code is not compatible with ESP8266 
Lost some nerve on that but it was some step forward. Now I’m using the code found WifiShield with arduino uno compiling error - #11 by kreggly
After uploading ESP dedicated code I’m getting this error read in 9600 baud:
[519] Connecting to name of my network
[1530] Failed to disable Echo
Read that it could be connected with old AT firmware or power supply. Newest 1.5 firmware has been uploaded, power supply replaced to stable one used for external HDD connection and 5V dropped down to 3.3V via YwRobot module. No positive results. Even worst due to the fact that ESP is not reacting on AT commands. Just showing in 74880 baud:
ets Jan 8 2013,rst cause:2, boot mode:(3,6)
load 0x40100000, len 1856, room 16
tail 0
chksum 0x63
load 0x3ffe8000, len 776, room 8
tail 0
chksum 0x02
load 0x3ffe8310, len 552, room 8
tail 0
chksum 0x79
csum 0x79
2nd boot version : 1.5
SPI Speed : 40MHz
SPI Mode : DIO
SPI Flash Size & Map: 4Mbit(256KB+256KB)
jump to run user1 @ 1000