I agree with Cheryl O. in large part.
I am married, but not to my son's father. However, my son's father and I are really good friends, with NO DESIRE to reunite as a couple. That ship sailed a long time ago. But nonetheless, he and I remain great friends, and we communicate regularly about our son. This is healthy and normal, or at least it's the way I want it. I don't want my son torn between parents who don't get along, who don't communicate, etc.
As for the gift buying, my son is 5. He can't go get gifts himself, he does not have his own money, etc. BUT he WANTS to give his dad gifts when the occasions arise. YES, he does make him little things, but he also wants to give his dad an actual gift... I usually shop while my son is at school, so it would be probable that I would get my son's dad a gift when my son wasn't there, and say it was from him. I think that's totally normal. AND I am also friends with my son's father, so I feel no guilt in buying him something nice. And since we were together for 16 years, I happen to know what he likes, so I try to get gifts that are meaningful not to us as a couple, but meaningful to HIM. But I could see how it might look like I'm going out of my way to get a 'special' gift, but that's just what I do with everyone. I'm a 'thoughtful' gift buyer, so I like to get things that I know people will like. My son's father also doesn't feel guilty getting me a gift for holidays, and saying it's from my son. I don't see anything wrong with this. And my husband totally gets it and is fine with it. He knows this man will be in our lives for as long as my son is in our lives, and it's best for everyone to get along.
On the other hand, there does seem to be a little more going on in your fiance's ex's agenda. Calling or texting just to talk, because she's bored, well, that may be overstepping a bit. I do detect a tiny note of a little something more going on with her... but it sounds like your fiance isn't reciprocating, and as such, he doesn't see a reason to make a big issue of it, which could disturb the balance. These co-parenting relationships can be delicate. I would say that if you trust your fiance, and HE isn't the one initiating anything fishy, then you need to let this go. He can't control his ex. But he can control himself, and it sounds like he is. So if I were you, I'd let this go.