Spheres -- A country in your sphere of influence provides a certain amount of its economic strength to yours, in addition to being your allies. How much strength depends on your investments.
Annexing countries -- In the specific circumstances you mention, you can add India to the UK via the decision "Empress of India" and the periodic event "Doctrine of Lapse." For Germany, any country of German culture in your sphere will be added when you enact the decision "Three Hurrahs!" In most case, however, war is required.
Colonial Life Rating -- Two techs and an invention -- Prophylaxis against Malaria (invention under Medicine), Machine Guns, and National & Imperialism all make it easier to colonize.
Egypt -- If you sphere a country you cannot attack them. Thus, if you want to conquer Egypt, just use the appropriate war goal.