Key points.
1. UFW allow specific IPs:

ufw allow from 123.456.789.0/24 to any port 3306

2. MySQL add remote users (e.g. only allow INSERT):

GRANT INSERT ON DB_NAME.TABLE_NAME TO 'REMOTE_USER_NAME'@'%' IDENTIFIED BY 'REMOTE_PASSWORD' WITH GRANT OPTION;
FLUSH PRIVILEGES;

3. In PHP, use quotes around variable names;

$sql = "INSERT INTO TABLE_NAME (FIELD1, FIELD2) VALUES ('$VAR_1', '$VAR_2')"

Some debug tips:
1. Check if PHP functions for MySQL are available

echo var_dump(function_exists('mysqli_connect'));
echo var_dump(function_exists('mysqli_query'));

2. Check active connections in MySQL

show processlist;