(((TRUST))) issue is the problem here Granny you don't trust the man that's the bottom line. To the point where he's now reduced to being called a so called boyfriend and you've been reduced to seeking out was to spy on him like a hired private eye to spy on him. Yes there's a strong reason for you wanting to do extensive detective work on this man and you might say it's none of our business but when you post on this sight you make it our business. You really need to stop playing in your head and tell the man that you don't trust him, so that you and him can bring your issues out in the open and stop playing (((spy-vs-spy))) because not trusting your partner brings a miserable and upsetting attitude in to the relationship. Now let me say this before I go back into Internet world, have no (((trust))) is only a slow miserable (((rust))) to a corroding relationship that's doomed to end.
You can read you boyfriends' text message without his phone on your computer by installing a mobile phone spying software. Be aware that this may bring up some invasion of privacy issues if you ever fall out, so you should always seek professional advice before doing so.
You can't unless he has a smart phone and you buy a device that enables you to. Go to best buy. Also, you could check his records online to see if he has lots of texts to an odd number. You could also put a voice activated recorder in his car.