Thanks for asking, Alan, that's a critical question.
The alpha-delay plot is the most important one. The key thing to realize is that you might not be able (or rather not want) to trade into a factor-portfolio immediately on the first day, the primary reason being transaction costs / slippage. Say for example you have a factor with an IR of 10 on the first day and then of -2 on the day after. So you better trade into the target portfolio extremely quickly (ramping up huge costs). But then you also have to trade out of it extremely quickly or you're bitten by it the next day. That example is a bit extreme but the same mechanism is at play at longer time-scales.
Imagine you have a factor that turns over 50% a day but you set a turn-over constraint at 15% a day. What will happen is that you'll be constantly trying to catch up to the factor. As you're doing so, those older factor-portfolios that you were trying to target e.g. 5 days ago will also still linger around in the portfolio, because you can't easily trade out of those existing positions. So ultimately your portfolio will follow the factor to some degree with some lag.
That is why it's important to look at what happens if you were to trade your factor 1, 3, 5, 20 days delayed, because you will. Your specific factor looks like it has pretty stable alpha over time, those wobbles are just noise and I wouldn't read too much into them. I have seen many other examples where it's super high on the first day and the sharply drops to zero by day 3, that pattern is more worrisome. So that looks like a pretty good factor to me. From the exposures I would think it's fairly close to a standard reversal factor.
Anyway, from that understanding above, another related insight can be derived:
1. You shouldn't sub-sample your factor (e.g. trading it weekly or monthly) to achieve lower turn-over. As an example, imagine you emit a new signal on the first day of the month, but maybe we only trade on the 5th of that month. We would start trading into a 5-day old portfolio. We'd rather trade into something more recent. Instead, you can apply a moving-average to your factor (e.g. 5-day), that way you slow the factor down but it will still update daily. Although you actually don't need to fret too much about turn-over, as long as it has good alpha over several days, we will be able to capture it.
2. You shouldn't tweak the trading time. If your algorithm is sensitive to trading times, it's indicative of short-term alpha or some noise you're trying to overfit to. My advice is to set to always trade as close to the close as possible and never change it.
Finally, you can probably tell how our own thinking is evolving here (and I plan to do a larger post on this too). Given everything I've written above, I view this type of analysis as absolutely critical. A user could easily work on an amazing looking backtest with a Sharpe of 6 without realizing that it's super short-term and actually not interesting for our current trade horizon. My advice is to run this analysis as the very first and main thing when working on a factor/algo.