Regardless of extra-curricular activities there will always be politics. You cannot "parent" this out of people except by example from the top down and good hiring practices. It may be a good practice, but it is a personal practice -- it should not be enforced by an employer because it is an invasion into private life. Something like Google's 20% time is a great idea but difficult to get working and keep up.
Employee browsing the internet on company computer.
Best way to protect against false impressions is to not engage in questionable activities while at work on company time. If an employee doesn't play chess, browse facebook, or watch youtube while at work, they won't have any problems.
We never go and see what founder does with his desktop/laptop
If the founder wants to goof up, then fine -- but he is not the employee. Employees are the employees and they are responsible for their actions. Founders are not responsible to the employees. It is not mature to argue that "we never go see what the founder does".
I agree with this, you can remove his email-id from dl so that he can't send/receive mails , but don't block the account.Give him couple of days , so that he download/retrieve any income tax or payslip related documents. How can you suddenly won't trust an employee, just because he resigned ? Or at-least confirm with him before blocking the access.
None of that is necessary to send/receive income tax slips -- it should all be handed to the employee upon termination. Also, you CANNOT trust any employee who is not in your pay because they are free to work for a competitor. I work with co-workers who have horror stories of what ex-employees have done.
Also, keeping an email account open may be forgotten to be closed by the IT department and may also provide access to other parts of the corporate network which may allow for the ex-employee to sell secrets to competitors.
Shutting down email access is just best business and IT security practices common throughout the entire world. It is bad form to not shut it down.