Why not "se pravdou", since there's a consonant cluster beginning the word "pravdou"?
Honestly - no idea. :/ All I can say that while very often you can choose whether so put the "-e" there, in this example, you just can't - it would sound very weird.
Good idea. I suppose the reason is easier pronunciation. I thought preposition "SE" is used in front of words starting with letters s or z. Often also š and ž. Everywhere else is used "S".