Wir üben die Falltechnik und springen ab.

Because abspringen is a separable verb. In a normal main clause, the prefix separates from the verb and goes to the end:

• Wir springen ab.
• base verb: abspringen

So in Wir üben die Falltechnik und springen ab, the ab belongs to springen.

For the same reason: abspringen is separable.

In the infinitive, the parts stay together:

• abspringen

In a conjugated main clause, the verb stem is in the usual verb position and the prefix moves to the end:

• ich springe ab
• wir springen ab

So springen ab is the correct main-clause form.

Because both verbs have the same subject: wir.

German, like English, often avoids repeating the subject when two verbs are joined by und:

• Wir üben die Falltechnik und springen ab.

This is similar to English:

• We practice the falling technique and jump off.

You could repeat wir, but it would usually sound unnecessary here.

Because Falltechnik is the direct object of üben, and the noun is feminine.

• üben usually takes a direct object: you practice something
• Technik is feminine, so the compound Falltechnik is also feminine
• feminine singular article in nominative/accusative is die

So:

• die Falltechnik

German compound nouns usually take their gender from the last part of the word.

• der Fall = fall
• die Technik = technique

The whole compound is die Falltechnik because the final part is Technik, which is feminine.

This is a very useful rule for German compounds.

üben means to practice.

It can be used for skills, movements, music, sports, grammar, and so on. In this sentence, it means practicing a technique or movement.

Examples:

• Wir üben Deutsch. = We practice German.
• Sie übt Klavier. = She practices piano.
• Wir üben die Falltechnik. = We practice the falling technique.

Because they are both conjugated for wir in the present tense.

For many German verbs, the wir form is the same as the infinitive:

• wir üben
• wir springen

That is completely normal.

It is in the accusative case because it is the direct object of üben.

You are practicing what? → die Falltechnik

With feminine singular nouns, the nominative and accusative article are both die, so the form does not change here. But its function in the sentence is accusative.

Yes. German very often combines nouns into one word.

So instead of writing something like fall technique as two separate words, German normally makes one compound noun:

• Falltechnik

This is extremely common in German and is something learners see all the time.

No. In a subordinate clause, the separable verb usually stays together.

For example:

• ..., weil wir die Falltechnik üben und abspringen.

Here abspringen stays together because the finite verb goes to the end of the subordinate clause.

So:

• main clause: Wir springen ab.
• subordinate clause: ..., weil wir abspringen.