Does the row locking on slave database also apply to master database? In a transaction, for example,

START TRANSACTION;
SELECT count(*) as count FROM `order` WHERE user_id = 25286 LOCK IN SHARE MODE;
INSERT INTO `order` (`id`, `user_id`, `product_id`) VALUES (NULL, '25286', '36296');


we perform the SELECT LOCK IN SHARE MODE; the SELECT query will be executed on the slave database and lock a row.

Does the SELECT LOCK IN SHARE MODE also create a row locking on the master database so that the INSERT query will not run on a master database?
There is no communication from Slave to Master (aside from network protocols to receive the Replication updates from the Master.

Writing on a Slave is a no-no.  The basic principle of Replication is that the Slave will have exactly (except for a slight lag) the same data as the Master.  Writing to the Slave does not allow for keeping them in sync.

An exception is with Master-Master -- wherein two servers are acting both as Master and as Slave.  Still, writing to both leads to a lot of potential problems, and should be avoided.