Will the indexing affect insert/update/delete operation in Mysql
Of course. 

The choice of primary key can greatly influence all select/update and insert operations. It's because your data will be PHYSICALLY placed on the disk by the order of the primary key. 

Modern hard drives provide great transfer but only if you read sequentially. When it comes to reading random spots on the drive, your HDD  can only access 75-150 different areas per second. So when it has to "jump" around when reading/writing data that can't be written/read sequentially ( due to bad primary key chosen ) - it will significantly affect performance.

Additionally, when inserting, mysql server has to recalculate indexes and when you overindex your table, this can kill your performance.

Choosing your indexes - and particularly your primary key - is one of the most important choices when designing your tables. Most performance problems can be fixed by addressing indexes.