From what you have written he has made work his priority. This is not your “own doing.” If you had it your way, you and he would spend more time together. He tells you repeatedly that he’s going to change. You said it best: he is “basically a lot of talk without action.”
Not many people would be willing to tolerate “a lot of talk without action” for very long, especially in a new relationship. You seem to have given him sufficient opportunities to change his behavior, yet he has not.
From your letter, it seems as though you and he have already parted ways and you are considering whether or not to give him another chance. Only you can answer that question but before you do, have an honest discussion with him about the various problems you have had with the relationship. If you don’t, and you decide to give him another chance, then he will likely continue the same behavior. If he can get away with “all talk and no action” his track record shows that he probably will.
If you decide to reconcile, inform him that he will have to prove that he can change by actually changing. Be specific about how you want him to change. The more specific you can be about the needed changes, the more success that is possible for the relationship.
To the question of cheating, it’s not clear from your letter that he is. Having friends on Facebook with people you disapprove of does not equate to cheating. Nor is it necessarily a sign of betrayal. Hiding his friends list would be a form of betrayal. He is not hiding his friends from you.
Having said that, since you expressed your dissatisfaction and he continues to keep his Facebook friends, then this could be a problem for the relationship. If it’s a problem for one party in the relationship, then it’s a problem for both. The question then becomes should his having certain Facebook friends be a problem for you? Unfortunately that’s not something I can determine from a short letter. I would have to have much more information about why you see it as a problem before I could determine if your concerns are warranted.
Gradually, you and he were spending less time together but it is difficult to determine why. It could have been the dynamic of the relationship. Early on in the relationship you and he were not spending much time together. As you stated, there was no “honeymoon period.” It might also have been a sign that the relationship was degrading. I believe that it might have been the latter but I can’t know for certain. The fact the you decided to end the relationship (at least temporarily) also supports the idea that the relationship wasn’t going well.
“Should you take him back?” is your primary question and regrettably I can’t answer that for you. If he is unwilling to change and he continues to put all of his needs before yours, then no, you should not take him back. A one-sided relationship would be unhealthy and unsatisfying. Relationships need to be balanced. If you continue to struggle with how to approach this relationship, then you may want to consult a therapist. Click the find help tab to locate one in your community. I wish you the best. Please take care.