I am attending two conferences, back to back, in two different EU countries. I have time to apply to only one visa. Is it possible to travel from one Schengen country to another for this purpose with no problems?
Yes, that's the purpose of the Schengen Zone; to encourage inter-European trade and commerce.
You need to apply in the EU country that you will be spending the most time in and if it's a tie in terms of days, you need to apply to the first country you will be landing in.
Yes, your Schengen visa is valid throughout the whole schengen area. You can see the official statement
A Schengen visa is a short stay visa allowing its holder to circulate in the Schengen area. The Schengen area covers 26 countries ("Schengen States") without border controls between them. These countries are: Austria, Belgium, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden and Switzerland.
A Schengen visa is an authorisation issued by a Schengen State with a view to:
transit through or an intended stay in the territory of the Schengen States of a duration of no more than 90 days in any 180 days period ("short stay visa"), transit through the international transit areas of airports of the Schengen States ("airport transit visa").
in the official EU commission website, here.