Can we shrink datafile of a database which is configured with log shipping I am using MS SQL Server 2012 version RTM, below is our environment,

I have a primary database Server A and Secondary Database Server B Log shipping configured on A to B of a database, 

1) Database size 500 GB, We would like to delete old data and make it to 250 GB, Can we do this without breaking of log shipping?

2) After this we need to shrink the data file not log file, Can we shrink data file without breaking of log shipping?

If we do shrinking do i need to stop log shipping jobs or will it break log shipping configuration?
No, shrink won't break Your log shipping configuration. But You must be aware that both shrink (and rebuild/reorganize You will have to do afterwards) will make Your transaction log files grow a lot. All of those operations cause a lot of I/O load that is logged to transaction logs.

This, in practice, might mean that while Your log shipping won't break, it will make restore last a lot longer, depending on Your backup/copy/restore jobs frequency of course. That might lead to secondary falling behind a bit till shrink's (and defrag's) end.

Remember that shrink has serious issues, read Paul Randal's post about it, if You haven't already:

http://www.sqlskills.com/blogs/paul/why-you-should-not-shrink-your-data-files/

http://www.sqlskills.com/blogs/paul/a-sql-server-dba-myth-a-day-930-data-file-shrink-does-not-affect-performance/

https://www.brentozar.com/archive/2009/08/stop-shrinking-your-database-files-seriously-now/