Most sensible post on the entire thread from@Strawberriesaregreat - she sums it all up beautifully OP.
His messages COULD be interpreted as 'loving' but to me, they read as suspiciously hyperbolic.
"All I've ever wanted is for you to be happy" is codswallop innit. Only a hopeless romantic or a teenager would be taken in by it.
OP - did you ever just TELL him - face to face - that you are concerned/pissed off that it feels like he's refusing to introduce you to his mates?
That his rejection of your facebook tag, his single status etc, while a small matter, is big TO YOU because his excuse is that he is prioritising his ex's feelings over YOURS (the woman he purports to love & want to make happy!?)
That you wonder why he snapchats, then minimises/denies snapchatting, Sports Woman, when he knows she holds a torch for him & you feel that's a cruel thing to do to her, & a mixed message to you? That he is hurting YOU by refusing to cut it out? The person he "always tried to support"?
Because if you have, & all you are getting back is this word salad, I think you should dump him without compunction.
However ... if you have NOT - & I suspect you haven't, because - forgive me - you seem to have been doing a lot of passive-aggressive hinting, but don't seem to have clearly stated your wishes - he may have a point with "is everything always going to be a test?"
If you have not told him, directly & simply, that these 3 things piss you off, how is he going to know?
Please don't feel criticised here OP: it's kinda understandable that you're scared of stating your needs directly, because you are so scared of being rejected again.
This is why you are measuring yourself against this Sports Woman, instead of measuring HIM.
You are scared that history will repeat, but, sadly - if you 1) do not use plain speech, in person, with him & 2) continue to "test" instead of "state", you are going to remain unhappy & he - if innocent - will remain confused, & pushed away.
Stop competing with Sports Woman, & start addressing him clearly & directly, And not by text.
Here's a vital resource to help you understand why competing with another woman is self-defeating - www.chumplady.com/2012/04/the-humiliating-dance-of-pick-me/
Once you've read that, spend some time - a LOT of time! - noodling round ChumpLady's excellent site. I can't think of a better resource to help you heal from the wound your Ex inflicted on you. If you combine it with the Assertiveness book I linked upthread, you will be well on the way to achieving ChumpLady's goal for all the cheated-on: "Lose a Cheater, Gain a Life".
She's also hilarious, which helps.
You are gonna be ok whether you choose to let your current guy stick around or not OP. Once you start truly valuing yourself, other people's fucks-up (if he HAS fucked up, & I rather suspect he has, because it's all mouth & no trousers right now) you will lose the need to 'test' men, because you will be so much more secure in yourself. That's 100% more valuable than a relationship with someone who is as ... evasive as this man has been. 