I know you're trying to teach a specific Danish tense, but the English translation provided doesn't sound quite right to me. If all the finding will taking place on Saturday, we would simply say I will find more on Saturday. If the finding is a more continual, you could say I will have found more by Saturday. I'm not sure which the Danish sentence is saying.
The future perfect doesn't have anything to do with continuity. It means that something will happen after something else happens or after a specific point in time, eg. "I will have finished my assignment by the time class starts Monday morning." And it works the same way in the other tenses, eg. "By the time I got to Phoenix, she had left."
Apparently, they simplify this tense in Danish by just using the present perfect. That was a surprise to me, as well.
Maybe I don't fully understand your wording, but indeed the perfect tense(s) is related to continuity; The name 'Perfect' simply means that the activity was completed/finished, aka is not continued/-ing.
The exercises are cumbersome and sometimes wrong in both languages, and honestly I (being a native Norwegian, which is really close to Danish language-wise) need to stop and think longer to decode the Danish than the English. It's the same in other lessons; The passive verb usage contains exercises that nobody would use in practical life, unfortunately ...
It's in present perfect tense, but as with any present tense in Danish, with a time expression it is the future tense (or here future perfect). "Jeg vill have fundet" would mean "I would have found", which would be conditional perfect, "Jeg vil have fundet" is accepted though
This unit confuses me. My go-to-Dane, who's pretty good with language, thinks that the sentences constructed like this one (instead of e.g. "Jeg vil have fundet flere på lørdag") may technically be kind of correct, but are at least really bad style. I'm not sure why this unit is specifically devoted to teaching that construction.
I agree. It's ridiculous to teach something that isn't used. In the lesson tips they say "we don't use this, but you do in English so here's how you would do it in Danish" - even though you'll never hear anyone say it. But, you can say it - even though you won't sound right.