Is the ai in j'ai and finirai (I am assuming they are the same) pronounced exactly like the -er in infinitives: are manger and mangeai pronounced exactly the same?
Both are the same
close-mid front unrounded vowel (
Please see the rest of my answer for an audio example of the pronunciation -ai. The third segment of the dictation also has various samples of the pronunciation of the -er ending (for example, Ils se sont entraînés à en déjouer les pièges.)
That said, it seems not everybody uses this pronunciation of -ai so the people who pronounce it like -ais1 will indeed make a difference between -ai and -er (on which there is probably little discussion)
1. They're wrong :-)
No, there's a slight difference in pronunciation between the two forms (although some people in france can't pronounce it differently) :
mangerai (will eat) is pronounced [ɛ] while manger (to eat) is pronounced [e].