Whenever Jabba says something to Leia in Huttese she never seems confused at all - she seems to understand what he's saying. Also, when Jabba gives Leia an order or talks to Leia does he do it in basic or huttese?
Probably, but not necessarily
While Leia reacts to Jabba directly, there isn't a scene where she is doing so verbally that Threepio is not translating.
From the transcript:
Later, Leia may be reacting as much to Jabba's physical actions as verbal ones:
Which is pretty much the last bit of dialogue for her and Jabba. They don't seem to have much to discuss after this...
However, considering the following:
It's not unreasonable to assume she understands the language. But from the movies at least, no confirmation that she does.
According to C-canon, Liliac (and Jabba) spoke Basic.
Please note that if you search for "Huttese" in book, you will see that it's very frequently mentioned that Hutts speak in Huttese specifically in various situations (including to Boba Fett). Therefore, the lack of such clarification here makes me assume it was Basic.
There is no mention of Leia understanding Huttese, though she does seem to understand Jabba's comments. She is never spoken to in Huttese or professed to understand Huttese during the EU. She can speak Ubese, which she uses to speak to Jabba in Return of the Jedi.
Jabba, however, to answer the question put in the comments, is shown to both understand and speak Basic during the EU. Putting aside the two occasions DVK mentions in his answer -as I tend to side with SSumner on this, and did so when I read the trilogy in question years ago, that Jiliac and Jabba are in fact speaking Huttese and assuming that Solo understands as he answers - in Shadows of the Empire, Jabba speaks Huttese to Prince Xizor, who requests that he speak Basic. Jabba replies, in Basic, "as you wish," and continues the conversation in that language.