Is Mining Bitcoin While The Price is Low or High better? I have a few questions:

Does the reward for Bitcoin increase/decrease when the price goes up and down?
Is it more profitable to mine when Bitcoin is down, or when it is up?

Thank you!
Does the reward for Bitcoin increase/decrease when the price goes up and down?

The reward for mining a bitcoin block is:
(the current block subsidy) + (the fees from the included transations) = (the block reward)
The block was originally 50 BTC, and this amount is cut in half every 210,000 blocks. At the time of writing, it is 6.25 BTC.
The price is an extrinsic property, it has no affect on the number of BTC included in the block reward (though obviously the dollar value of the block reward will change, as the price changes).

Is it more profitable to mine when Bitcoin is down, or when it is up?

Profitability entirely depends on the miner's costs, and revenue. It is a highly competitive free market.
When the price drops, some less efficient miners may become unprofitable, since costs are usually payable in fiat currency, and the block reward is realized in BTC.
When the price increases, miners will see a larger profit in fiat currency terms, but this also means that less efficient miners may join the network (as they are now able to operate profitably), thus netting the already-operating miners a smaller portion of the total rewards over time.
It is a constant push-and-pull. A higher fiat price per bitcoin will mean more revenue (denoted in fiat), but also more competition. We might expect this effect to roughly cancel out, so that profits trend towards zero on average (if they were higher than zero, we would expect more miners to join the network, to take a piece of this profit).