How does the game determine how many charges a weapon will get if you enchant it with two different effects? For instance, if I enchant a sword with Soul Trap for 1 sec, which would have thousands of charges, and max fire damage, which would have like 50 charges. How many charges would the weapon have?

There's no real way to calculate it, besides going to an enchanting altar and trying it out for yourself. For instance, I have maximum fire and shock damage applied to my Daedric sword that use right now, and I have about 97 uses of the thing, because I used a grand soul in the Black Star. Remember to use grand souls while enchanting, the benefits and effects will be so much higher and so much better.

Fewer than for fire alone. Try it. It seems to base charges on whatever takes most.

You can buff your enchanting to get more charges out of soul gems, but that's about the only way to do it.

It would have thousands of Soul Trap charge and 50 of fire damage charge.

Errr, no.