Interested in extending or renewing your Indian tourist visa? You can apply for tourist visas only at Indian Visa Application Centre or at an Indian mission outside India. In other words, it is not possible to get a new visa while being India.
You cannot get a Russian visa while you are in the country nor extend your current one. Russian embassies and consulates outside the Russian Federation are the only ones issuing these visas.
Bad news first: It is not possible to renew, extend or change the type of your Chinese visa. However, you can apply for a new visa while staying in China. You will need to apply at a Public Security Bureau Exit and Entry Administration office.
To prolong your stay in Vietnam, you can do a visa extension or a visa renewal. Regardless of what you chose, you must apply a couple of days before your visa actually expires since both processes take about 5-7 working days.