DISCLAIMER: doinkies isn't a native speaker of Japanese so I might make some mistakes in this post or not be quite sure about some things. ^^;; My Japanese ability isn't too doinky though...
Hi Vicki!
For the first sentence, "minikui" is an adjective and it isn't the object of the sentence. So there's no "o" in this sentence. Instead, you say wa because that indicates the subject (the subject being "your face" in this case). So the correct sentence is:
あなたの顔は醜いです。
Anata no kao wa minikui desu.
As for the second sentence, while 必要があります (hitsuyou ga arimasu) is a literal translation of "I need ~", in this sentence, doinkies would use ほしい (hoshii) instead. ほしい means "to want/desire (something)" or "to be in need of".
So the second sentence would be (私は)弁護士がほしいです。([Watashi wa] bengoshi ga hoshii desu.)
As for when to use "watashi wa"...if it's clear that you are referring to yourself and not to someone else in a sentence, you don't need to use it.