1. “How can I figure out what my future $DIBS rewards will be from the Piggybank?”

Simplified example for a non-debt phase: say you have 1 $DSHARE staked out of 10 total $DSHAREs staked in Piggybank, so you will get 10% of the total $DIBS emissions.
So, for this example we are assuming that there is a total circulating supply of 10,000 $DIBS, the current expansion rate is at 4%, and therefore 400 $DIBS will be emitted. You would get ((0.04 * 10000) * 0.8) * (1/10) = 32 $DIBS. With current regulations, this is the distribution breakdown: -80% of printed $DIBS goes to $DSHARE stakers. -15% goes to DAO-fund. -5% goes to the devs.
Formula to calculate your rewards: ((ExpansionRate * CirculatingDIBSSupply) * 0.8) * (YourDShareStake/TotalDShareStaked)

2. “How long will it take for DSHARE to pay itself off from $DIBS rewards, based on current prices?”

This will vary constantly as the APR in the Piggybank fluctuates, along with other variables such as the price of $DIBS.
For a quick estimation, however, you can do the following:

1) Take the total APR shown in the Piggybank, and divide that by 365 to get the daily APR. (In this example, we will say the daily APR is 5%.)

2) Multiply that daily APR by the current market price of the total Dshare you have staked to see what your daily rewards are.(In this example, we have 5 Dshares, each worth $500, for a total amount staked of $2500. Your daily return is $2500 * .05, which comes out to $125/day.)

 3) Take your initial buy-in price for Dshares, and divide it by your daily rewards. If you bought these 5 Dshares at a higher price of $700, for example, in the current market conditions you will recover your initial investment ($3500) in 3500/125 = 28 days.

3. “Does a higher TVL mean a higher APR?”

The more TVL in the pool, the less APR (there's more people getting the same piece of the pie), but the higher the price of the reward (the pie) the higher the APR (better quality of pie). In other words, although the same rewards are diluted across more investors, if those rewards have a higher dollar value because of the increase in TVL, then it can actually lead to a higher APR as well.