iPhone to an external monitor.

Yes, depending on your model you can connect your iOS device to a monitor

http://www.apple.com/shop/product/MD826AM/A/lightning-digital-av-adapter

again, depending on model you can connect a variety of devices to it.

http://www.apple.com/shop/accessories/all-accessories/mice-keyboards?page=1&fh=4 0a2%2B43bb

While you can connect an iPhone to a monitor, you cannot control it from the monitor in any way.

Al inputs and controls must be done on the iPhone itself, though you can see the iPhone's screen on a monitor or TV while you do it.

http://www.apple.com/shop/product/MD826AM/A/lightning-digital-av-adapter

Use the Lightning Digital AV Adapter with your iPhone, iPad, or iPod with Lightning connector. The Lightning Digital AV Adapter supports mirroring of what is displayed on your device screen — including apps, presentations, websites, slideshows, and more — to your HDMI-equipped TV, display, projector, or other compatible display in up to 1080p HD.

See the article suggested by Apple above

You can take a look also at this article to connect your iPhone wirelessly How to AirPlay content from your iPhone, iPad, or iPod touch - Apple Support