Are any inference providers currently making profit (on inference, I know google makes money)?
Pretty much every major American inference provider claims to make a profit on API-based inference. Consumer plans might be subsidized overall, but it's hard to say since they're a black box and some consumers don't fully use their plans
Google definitely makes money in other areas. Do they make money on inference?
Selling inference is not fundamentally different from selling compute - you amortize the lifetime cost of owning and operating the GPUs and then turn that into a per-token price. The risk of loss would be if there is low demand (and thus your facilities run underutilized), but I doubt inference providers are suffering from this.
Where the long-term payoff still seems speculative, is for companies doing training rather than just inference.