Is there a tool or plugin in QGIS to extend line features up to their intersection point?
Perhaps you can do it with some of the CAD plugins of QGIS. For sure you can do it with Kosmo GIS http://opengis.es/
Select to linestrings which should be extended and use the Expand lines until crossing tool from the CAD toolbox. CAD Tools extension must be activated first from the Extension manager.
Click on the map.
For the second case use another CAD tool "Extend line"
Extend to nearby feature option suits for this use case
Click close to the line that should be connected
CADDigitize now comes with a trim/extend function.