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Cavalry can obviously do ride by attacks. I am wondering since he has virtuoso can I charge a target, shoot another one along the way and trigger the multiform star action? Also when determining free strikes does a cavalry model use it's mount or the lance?

You can't do both a Ride-by attack and a Charge.
You can't charge and do its special attack (multi-fire) because charging means you have to make your initial melee (or ranged because of Gunfighter) attack.
Special attacks , special actions and such are instead of initial attacks
You can't make free strikes with the lance because you may only use it for Charge attacks

But I can move, use the multifire, continue moving then make a single noncharge attack right?

No, as once you do the Multi-fire special attack, you can't do your initial melee attack.
The lance only works on the charge, the thane has no non-charge melee attack to use in your scenario anyway

I can't use the mount?

Most cavalry models can't just "use the mount" no, it's only to make Impact attacks (that happens during a Charge)
Some models have a rule called Combat Rider that allows them to use their mount in the way you think, but the Destor Thane doesn't have it IIRC

Thank you so much!