Official QIWI developer page: https://developer.qiwi.com/ru/qiwi-wallet-personal/#intro
Source: https://github.com/Shnapik/Qiwi-Api-Class-PHP/blob/master/src/Qiwi.php
Official QIWI API page (without send...() functions): https://github.com/QIWI-API/bill-payments-php-sdk

Connection:
require_once 'path to file Qiwi.php';

$qiwiData = [
    'phone' => 'qiwi phone number without +',
    'token' => 'qiwi api token'
];

$qiwi = new Qiwi($qiwiData['phone'], $qiwiData['token'], false);

Basic function:

$walletBalance = $qiwi->getBalance();
var_dump($walletBalance);

getProfile() - Information about account
getIdentification() - Information about account identification
getLimits() - Active limits, that account has
getRestrictions() - Shows if there are any restrictions and information about them
getPaymentsHistory() - Payment history
getPaymentsStats() - Payment statistics between chosen dates
getPaymentInfo() - Information about current payment
getCheque() - Cheque of current payment JPG/PDF
getBalance() - Current balance
getTax() - Tax, that you will pay by sending moneyy to a current account
getBills() - Check your bills
getMyNickName() - Shows account nickname
sendIdentification() - Sends identification to QIWI (didnt check it though)
sendMoneyToQiwi() - Send money without confirmation to someone
sendConverted() - Transferring funds to a foreign currency account QIWI Wallet with conversion from your ruble account.
sendMoneyToOther() - Send money by card num.
sendBillPayment() - Pay summ by bill number