yes there is 3rd person the settings such as 3rd person, crosshairs Ect. are set by whatever difficulty you have chosen.
this sound's more like a bug i have encountered a really long time ago. so long ago i dont remember what was even causing it. this was not on this particular mission it was in a few old versions of SP but i think it was on my end at the time i had some files missing or something.
but i have not encountered that bug in a really long time.
if you would like to post a more detailed description of your install i would be more than happy to help.