If your client is unable to give you a proper database dump, then whatever task they're asking of you will take far longer and cost much more than anyone should be willing to tolerate.
Is there a way I can restore the database with only ibdata1 file?
⇢ Yes, but not without a remarkable amount of work. People who are not trying to save a multi-billion dollar company from lawsuits should never have to do this.
Shall I need any other files apart from .frm files and ibdata1 file in order to restore the database?
.frm files contain the definition of a database. The
ibdata1 file can contain many databases (depending on how MySQL was configured). If you must restore the database with only the
.frm files, you will need all of the files in their correct directories. From there you may be able to restore so long as your version of MySQL is either exactly the same or just slightly newer than the version the client is running.
Note that restoring
.frm files from a foreign MySQL installation will obliterate any databases you already have configured on the receiving machine.
Suppose I can restore the database using just ibdata1 file or I get .frm files in future, Do I need to install a version that matches the client's MySQL version?
⇢ This was answered in the previous bit. While it's technically feasible to take an
ibdata1 and accompanying
.frm files from earlier versions of MySQL and upgrade them, there can be problems when jumping a large number of releases. Going from MySQL 5.3.x to 8.0.24, for example, is almost guaranteed to fail unless the source database is structured more like a CSV than a series of relational tables.
If your client is able to access the MySQL server, have them create a proper backup with MySQLDump and provide that file to you. This way you do not have to worry as much about versions or anything else. Everybody will save time and hassle.