Battery University is a very good site for explaining battery technologies and how batteries behave. Fast Charging does damage the battery life, but this can be mitigated somewhat - generally by not allowing deep discharge or fast charging above 80% and efficiently discipating heat.
IMHO you are absolutely right that manufacturers of cellphones design ...
In theory, yes. Charging quickly means there will be more heat produced which is bad for the battery cells.
However, most batteries are equiped with controllers that make sure that the charging process runs smoothly to avoid reaching temperatures that would be detrimental to batteries.