When ETH value drops does the NXRA value also drop?

It depends on the situation. If both ETH and NXRA increase in value at the same rate, your holdings in each remain the same, and your overall value increases. If the ETH value rises faster than NXRA, you will sell some ETH for NXRA to balance ratios and vice versa. 

You can think of LP as an automated balancer for your tokens. 
You put in NXRA and ETH, their ratios will automatically adjust to balance the dollar value. 

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