When comparing a stock's price to a previous price, does the bot compare the high and low price of the day, the open price, or the close price?

When comparing price based on a look back period, the platform uses the stock's closing price.

When comparing a stock's price to a prior time, will it compare any pre or after-market pricing?

No, only the market close is referenced.

Can I select a time period of less than one day to compare?

No, only daily closing prices can be evaluated.

Can I specify my own "x day count" as opposed to being limited to the values listed?

No, at this time, you can only use the options offered in the individual decision recipe.

When comparing the current price to a previous price, does it only measure the price at the time the bot ran, or does it factor in prices between scans?

It is calculated only when the automation runs.