There is RemoDroid - nice, but I can't remotely tap.
There is TeamViewer for android - nice, but it's only for controlling (not for being controlled), at least for my device.
What program should I use to remotely administer the device (see screen and tap remotely)?
Primary use case is to assist installing and configuring some complicated application (like SIP client):
Just Install FooRemoteApplication: I'll connect and help you to install this.