You are correct, the tags you are talking about are likely Performance Equation tags, which were a precursor to Analysis which is definitely the recommended option. Both AF Analysis and PE Tags use the same syntax, so simple calculations using data from other tags would be effectively the same between both, the main difference is that AF Analyses add a lot more functionality that are unavailable with PE tags, such as Event Frame Generation, Rollup analyses, and SQC. Another one of the biggest advantages of using Analysis over PE tags is that since it utilizes AF attributes, you are able to make use of data coming from non-PI sources in your calculations, and you can also use analysis templates to allow for more widespread deployment of calculations. The analysis service also offers better performance and makes backfilling calculations a lot easier to do. If you're looking for more information on AF Analyses, KB01123 is a great resource.
For your second question, the analysis service needs the configured trigger criteria to be met for it to write a new value to the tag. If you are using natural scheduling but there is no data coming in, then the analysis would not be able to trigger, but a backfill would be able to go back and apply the calculation if the older data exists. Based on your earlier comments about your test system it seems like this is likely the case.
Let me know if you have any more questions!
Thanks David. I think there is an issue with the PI-PI interface - it is a fairly new test environment so hopefully once that is fixed I will be able to test this.