Learn Italian: Vorrei testare il software con te, ci puoi contare. - I would like to test the software with you, you can count on it.

Here, ci means "on it". In Italian, you "count on" something using the preposition su (contare su). The pronoun ci can replace su plus an object or idea. So instead of saying puoi contare su di esso (you can count on it), you just say ci puoi contare.

Can I attach ci to the end of the verb instead?

Yes! Because this sentence uses a modal verb (puoi) followed by an infinitive (contare), you have a choice. You can put ci before the conjugated verb (ci puoi contare) or drop the final -e of the infinitive and attach it to the end (puoi contarci). Both are perfectly natural and mean exactly the same thing.

Since the lesson shows ci can mean "with someone", why does the first half use con te?

While ci can replace con plus a person, it doesn't specify exactly who that person is. Furthermore, because ci has so many uses, saying ci vorrei testare il software might be misunderstood as wanting to test the software "on it" or "in there". Using the explicit con te (with you) makes the sentence instantly clear.

Why use vorrei instead of voglio here?