Learn Italian: Dalla sedia puoi vedere l'acrobata sul trapezio. - From the chair you can see the acrobat on the trapeze.

Puoi comes from potere, which expresses that circumstances physically allow you to do something (the chair gives you a clear vantage point). You would not use sai (from sapere) because that refers to having a learned skill. You could potentially use riesci a (from riuscire a), but that usually implies overcoming an obstacle, whereas puoi simply states that the action is possible.

How would the sentence change if someone was standing in my way, but I still 'managed to' see the acrobat?

You would swap out the verb for riuscire a, making the phrase riesci a vedere l'acrobata. We use riuscire a rather than potere when we want to highlight succeeding at an action despite a difficulty or physical obstacle.

Since acrobata ends in -a, is it a feminine noun?

It can be either masculine or feminine! Many professions and roles ending in -ta or -ista (like acrobata, dentista, atleta) use the exact same singular form for both men and women. The apostrophe in l'acrobata hides whether the original article was the masculine lo or the feminine la. You only see the gender difference in the plural: gli acrobati (masculine) or le acrobate (feminine).