multiple TN Visas at once and what happens if you lose one

I am a geologist and currently have one TN visa for a US oil and gas company where I was travelling down to Wyoming/Montana for a few days at a time. I am no longer working with this company. I live in BC and plan on flying up to Alaska for a couple weeks at a time for work with a different company. I have some concerns before I head through customs though.

Can I have more than one TN Visa at one time?

Do I need to forfeit my old TN Visa before it expires (1 month from now)?

I may or may not have lost the copy of my current visa, is this really bad or no big deal?

Do I need to bring anything to prove I haven't been hanging out in the states for the last few months?

If anyone can help me on this problem it would be greatly appreciated. Also, should I bring my original paperwork and degree every time I travel to the US on a visa even after it has been issued and it is still valid?

I am a geologist and currently have one TN visa for a US oil and gas company where I was travelling down to Wyoming/Montana for a few days at a time. I am no longer working with this company. I live in BC and plan on flying up to Alaska for a couple weeks at a time for work with a different company. I have some concerns before I head through customs though.

Can I have more than one TN Visa at one time?

Yes

Do I need to forfeit my old TN Visa before it expires (1 month from now)?

Yes, its not valid since you're no longer employed with the company. Surrender it to Canadian immigration.

Also if you entered on the basis of that TN when you were no longer in that position, you would be committing fraud.

I may or may not have lost the copy of my current visa, is this really bad or no big deal?

Do you mean the I-94 card?

Do I need to bring anything to prove I haven't been hanging out in the states for the last few months?

The I-94 card. CBP can issue a replacement.

If anyone can help me on this problem it would be greatly appreciated. Also, should I bring my original paperwork and degree every time I travel to the US on a visa even after it has been issued and it is still valid?

No.