[carlosalbffgomes]

So in the case of Voxalot, does it act only to initiate the multimedia session and and does no proxying?

Yes, if you have configured Voxalot to use re-invite. This happens if you have setted to 'yes' the 'Optimize Audio Path' in the Voice Service Provider configuration and 'Symmetric NAT Handling' to 'No' on the Member Details page. If you answer to the first option 'No' and to the second one 'Yes' (the defaults Voxalot configuration), then Voxalot will act as well as an audio proxy.

What happens when calls are passed through another provider via Voxalot, such is Betamax.

In theory, you may have a situation where Voxalot doesn't proxy your audio stream but your provider does it. This should happen if you dial a PSTN number, unless ENUM is used. You should try the best option that works for you. If you are at trouble, you can always use the Voxalot default configuration, meaning that Voxalot will proxy your audio stream as stated above. This should always work (no one-way-audio problem).
Regarding Betamax, I don't know because I've never used it. However, for the latency it seams to have (I know who use Voipbuster), it may be doing some audio proxying, but I can not confirm you that assumption.

Are there certain conditions when Voxalot will proxy and time when they wouldn't?

Normally, no. However, if you have configured the audio optimization and the voice provider you are using doesn't accept re-invite, you may obtain only one-way-audio problem. In such circumstance, you should use the default configuration stated above.

Same question for the Betamax end.

I don't know as far as Betamax is concerned because I've never used this provider.

Regards.