This is difficult, because I never learnt all the different names for the parts of English grammar when I was in school: only how to use them.  

Taking the commas first, strictly speaking you are possibly correct in that they could – or even should – be used in the places that you indicate.  However, stylistically it is very bad to split sentences up into very small bits unless absolutely necessary, and it is much better to have a flowing sentence than to implement punctuation that makes the prose harder to read.  

With the "Churchill devoted his time to educating himself" sentence, another way of putting it is to say that he allocated all of his free time to educating himself: if you used 'educate' it would indicate a future goal, not an on-going condition—there wasn't a point at which his education would be complete.  From the website you supplied, I think this page might help at 'Using Other Tenses in Conjunction with Simple Tenses'.  

Hope this helps.  On the other hand, I know that sometimes I make things more complicated than they actually are.