I understand that you wish to send SNS SMS notifications to your customers using SNS and have few queries around the same.
Please allow me address your queries:
1. "Can I send messages with it to the mobile numbers of peoples?":
>> Yes, you can send both 'Transactional' and 'Promotional' type SMS notifications directly to the phone numbers. You may refer to commonly asked question here at SNS FAQs (https://aws.amazon.com/sns/faqs/ ) under "Worldwide SNS" for more details.
2. "How much it cost?":
>> Charges for each SMS message actually depends upon the country to which you are publishing the SMS notifications. You may refer to the below mentioned documentation to know per SMS charge for various countries. Just enter the country to which you will be sending the SMS notifications to see the price:
3. "How many countries it is available?":
>> With Amazon SNS, you can send SMS (text) messages to 200+ countries. Please refer to the following documentation for the complete list of countries and regions.
4. "Can I integrate it with my website?":
>> Yes, you can integrate SNS with your website. AWS provides SDKs  in various programming languages. You can directly use these SDKs to integrate and publish SNS notifications. Alternatively, you can also use direct APIs  provided by AWS SNS to communicate with AWS SNS from your website. For example, to publish a message, SNS provides 'Publish' API call.
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Amazon SNS limits the amount that an AWS account can spend to send text messages (SMS messages) using the service. By default, the limit is set to 1.00 USD per month per AWS region to prevent abuse or misuse. However, this limit is a soft limit and hence, can be increased. Please refer to the below mentioned 'Premium Support Article' to know more about it.
Further, Please refer to the below mentioned link for monitoring your SMS deliveries (Success/Failure) with AWS CloudWatch.
I hope the above information is helpful.