I can definitely understand your concern and insecurity about this. From your description it sounds like he is actively flirting and is willing to show himself available by creating profiles with his picture, hiding at the same time the fact that he is married. There is a fine line between innocent flirting that can happen at e.g. the work place and the active flirting during which you "advertise" yourself. It seems that he may have somewhat crossed this line. Some of the other things that you mentioned e.g. about porn websites, may be indicating some issues with your sex life. Whether this is because of the post par tum phase (which can be very common) or because he is seeking something different I could not possible know.
The best thing I would suggest for you to do is to address this issue. Although you may be afraid that a possible conflict may complicate things, you need to uncover this and you both need to face it. I would therefore suggest that you had a serious talk about how this makes you feel, that you are wondering what is his motivation behind it, the insecurity that you feel because of it and about your future together. You need to be assertive but also keeping an open mind to be able to listen to his reasons without "blaming" him. You both need to understand where your relationship is going and whether you both feel that you can commit to that.
In many similar cases, engaging in couples' therapy may be very beneficial as you could use this space to express all your needs, feelings and thoughts without feeling threatened as you would have a professional facilitating these discussions. You could also help each other understand this better and find a common ground to work on. If there are communication issues or any sexual issues you would feel much "safer" and supported to discuss these through. So I would also suggest that after you spoke to him about this issue and how this affects you, you can discuss the idea of both of engaging with a couples' therapist.
I feel that you have very valid reasons of concern and you should give this issue the appropriate importance. No matter how uncomfortable this feels, you need to remove the blanket and face this, both of you.
I hope this helps.
Please feel free to share any feedback on these thoughts,
All the best