Do the searching and inserting capability of Sql Server 2008 engine in a table decreases with an increase in total rows in a table?
Do the searching and inserting capability of SQL Server 2008 engine in
  a table decreases with an increase in total rows in a table?


Yes the performance will eventually be effected but you can counter this with the addition of suitable indexes. Indexes will be easily be sufficient for managing the performance of tables that are ~50GB. If you get a lot more data in the future columnstore indexes and partitioning may be worth a look but they do require the Enterprise Edition of SQL Server. Columnstore indexes would require and upgrade to SQL Server 2012 or later.


  Is there per row data size limit?


A table can contain a maximum of 8,060 bytes per row but VARCHAR and NVARCHAR columns can be stored off row to provide more space. More details here