I don't think there's anything concerning here. I think you're still working on a somewhat shallow level, and once you start settling down and talking through your feelings about the deeper issues, some of your concern about flirtiness should abate. My therapist also accepted a birthday gift, some will not, others do, depends on the type of therapy, the client, the context, etc.

There are not a million set-in-stone rules about therapy. Don't date him, don't sleep with him, don't touch him inappropriately.... you know all this I'm sure. Tell him what troubles you in your day to day life, and if he helps you understand yourself and how to be less troubled and happier.... good, stick with it.

The part about always leaving happy? That's not necessarily how therapy goes, though it often starts that way. As you get deeper into the harder-to-change things, or the ones where you need more clarity, I'm thinking you may settle out of this.... focus on if he's attracted to you or flirting.

If you don't ever struggle, if all the sessions feel happy and easy... that would be a bigger warning sign to me. Therapy's a bit like the old saying, no pain, no gain. Not in a bad way, in a..... cleaning out wounds and sewing them up is important, but doesn't feel good way.