Can a database store a large numbers of record

That's what databases are for.

Yes.
Mind you it does depend on what you class as large as to which system would be best for the task.

Yes- Millions of records. I would recommend Microsoft SQL. If you are hosting a website try MYSQL - It's free.

I would recommend Microsoft SQL.

I assume you meant Microsoft's SQL Server. That's the product name. SQL is a copyrighted abbreviation for Structured Query Language. Which is a standard language for querying relational databases.