I think I need to disclose I'm a man before anything, so this is a male perspective. Here it goes:
Lol OP, seriously? all this overanalysis for something that is blindingly obvious?
If you're wondering what to do in such circumstances then perhaps you're not as bright as you think - sorry to say.
About the age difference, it sounds like you have an issue with it and looking for confirmation from others. You don't feel at ease with the issue obviously and you hope that others say it's ok to make you qualm your concerns.
My view? Yeah it is an issue. Not because of the difference per se, but because the guy is 60 years old. In all seriousness, how many "good" years do you think he has left that he can keep up with your lifestyle and interests? In 10 years you'll be 43, still quite young and active. Chances are he'll be 70 with a prostate, high blood pressure, arthritis and whatnot - probably taking naps 4 times a day and forgetting to take his pills. Okay, I may be overdramatic but you get the gist of it.
Also, 60 years old and falling in love? Not really..no..just an infatuation with a young virile pretty woman. Men like pretty women, men like independent women as well. However, that poses a problem for him, since you are independent it's hard for him to control you by offering financial security (which makes some women compromise on relationships). You already have a child, so tying you down with one is harder as well.
All that aside, the phone contacts issue, my oh my that's a seriously problematic man. Males do that in their teens, and then get sorted as they really grow up to become mature men. He hasn't got over that. He is totally insecure and that's because he acknowledges the age difference and the fact that he won't be competitive to the other male population for long. That's a serious issue, breach of your privacy etc.etc. I wouldn't stand up to that from anyone, let along a new relationship.
All that bullshit about seeing a psychologist etc. Do you know how many times men say they'll change? I do, every-single-time. Do you know how many times they do change? very-very-few. He is trying to appease you, he is in his posh way grovelling to you to persuade you. He'll just be cleverer next time. He was testing your boundaries and saw your snapping point. He will make sure to get around it next time in a more covert way, growing you more dependent first.
He is too old to change, period, end of, game over. He can pretend (and believe he has) for a long time, that's true. But deep down? He will always be uncomfortable and unhappy when you chat/interact with other men (let alone flirt - ha! imagine that! he'll have a stroke).
I think you may have been out of the game for too long and still think that the love game is played as when you were younger. He's much older, been through much more, and given his status he is used to people slaving under him - not being equal to him.
Also, all these flowers and crap, who really gives a toss? He is wealthy, so spending money doesn't mean anything. I would spend money on my wife if I was rich and I wouldn't bat an eyelid. Because it wouldn't make an effing difference to me. Acts like these have value when they come from people who perform them beyond their means, not within their means. It's going the extra mile that adds value. A man of his wealth and status (as you portray him) has money as no object to getting what he wants, so it's all more difficult as providing a persuading argument would require him to show bahavioural changes, not sending you Kew Gardens at your desk.
Also, about flowers and trinkets..you might find them romantic and feel your knees womble due to the romance. Men see them as the-things-I-have-to-do-to-soften-her-up. Flowers have no importance for me, I just see them as a way to improve my wive's mood when I've done something wrong heh.
Anyway, you're old enough and should know better but you have your blinders on. I'm not saying not to give the guy a chance, but know it's not going to end up in a soulmate relationships as your friends tell you (and you love to believe). Give him another chance and have some fun (if you can) but don't expect more and don't invest more emotionally until you are dead sure he has changed (hey miracles can happen I've heard - but never seen one). Just remember that it's much easier for him to find someone who will yield to his demands than make the effort to change. Sad but true. Once he "gets" you, he will lose interest probably.
Now (some) ladies of the forum, start your engines and fire at whatever you can construe (rightfully or not) as misogynistic and medieval in my viewpoints.
However, I do demand brownie points for actually putting in an honest effort to analyse and advise the OP on her situation. This was not a trolling attempt.
Having said all that, I'm out!