1. A show cause letter is a letter provided to the employee to explain the alleged misconduct. The warning letter is a statement of punishment to the employee when the employer is not satisfied with the explanation given by the employee to the show cause letter.
2. No implications. However, if the employer is unhappy over the reasons you cite in the response to the show cause letter, then they can take action against you. (Warning letter, Termination). The degree of punishment depends on the severity of the misconduct. Past misconduct can also be taken into consideration do decide on the punishment for future misconduct.
3. No. Your employer need not respond to your show cause letter if he is satisfied with your explanation. The employer has a choice of whether he wants to issue a show cause letter or to conduct a DI.
4. No you should not worry about the DI. Considering that you have not been provided with a warning letter for your previous offense, it is obvious that your explanation has been accepted and you have been given a chance to prove yourself. Put the incident behind you and move on.
5. If you continue coming late for work, your employer can issue you with a warning letter. If the employer is not able to tolerate your repeated late coming, then he may terminate you.
6. A DI is not mandatory although it is recommended. You can also be dismissed on the strength of a show cause letter, without a DI.
Show cause --> Warning (if dissatisfied with explanation)
show cause --> DI --> Punishment (Depending on severity)
warning letter --> punishment (repeat offenders)
In my opinion, I doubt that the employer will conduct a DI just to provide a warning letter as a punishment. The severity of the case is definitely taken into consideration before the conduct of a DI, which is cumbersome and expensive. For example, if the misconduct is of a minor nature that may equate to a warning letter as a punishment, then it wont require a DI. For more extreme cases that may end in termination, then it is best to resort to the DI to justify the need for termination.