1. Is there any limitation with Integration Cloud? Performance - CPU, Memory or Logging - only keep 1,000 logs or 3 months etc.
2. Can I create a web service in Integration Cloud? Like what I can with ESB.
Have you already checked online Talend Integration Cloud get started documentation:TalendHelpCenter:Getting Started with Talend Integration Cloud and TalendHelpCenter:Talend Integration Cloud User Guide?
CPU and memory is on your side as you are meant to have your Runtime installed on premise (you can have it on the cloud or both but it is a different pricing model).
From the link send earlier, you can actually export the log to an S3 bucket. The result is you can keep as much log as your organisation is ready to pay on S3.
Regarding the ESB, I believe it is on the roadmap but not ready yet (after this commercial link is stating the opposite https://www.talend.com/resources/ipaas-cloud-integration-platforms).