1- Does MySQL Community Edition (The free Edition) supports the following:
More than one CPU?
Full-text search?
Reporting services?
2- What is the size of the database? For example SQL Server Express allow to store 10 GB.
More than one CPU?
Yes.
Full-text search?
Yes.
Reporting services?
There isn't really a hard and fast equivalent functionality to MSSQL's reporting services - some options are outlined in this Stack Overflow question.
What is the [maximum] size of the database?
Many terabytes - there isn't a license limit like you'd see with SQL Server. An InnoDB table (individual table, not database) has a maximum size of 64 TB.