Do USB HUB Splitters power devices like mouses/keyboards etc?

Http://www.ebay.co.uk/itm/310350406188
Would connecting my mouse/keyboard/tablet work when connected to this HUB?
A friend told me charging his iPhone wouldn't work when using his HUB.

That is a non-powered hub. It takes the power from the one port on the computer (5V at 500ma total), and has to split the power to any device using that hub. This is ok for most keyboards/mice, since they use only about 100ma each. However, things using USB to charge, usually want all 500ma for themselves.
What you list is a "splitter". If you charge things, you need a "powered hub", one with an electrical wall plug, so it can supply 500ma to each and every port.
One like:
http://www.ebay.co.uk/...0975187459
has a power adapter.
or
http://www.ebay.co.uk/...0939423884

Also, watch out for USB2.0 vs 3.0 speeds. If your machine has USB 3.0 ports, and you want to maintain that speed, you would need a USB 3.0 powered hub, like:
http://www.ebay.co.uk/...0643659282
(that one has a US plug, but is universal power supply, you just need a plug adapter)

One final note, most of the powered hubs will also work without the power adapter, provided you do not need the extra power.So, for portable use, you can still plug in keyboard or mouse without the power adapter.