What is the difference between saying עוד and יותר in a context like this one?
Generally, יותר is for comparison (more than...), עוד is for addition (another one = עוד אחד, for example).
Basically, more=יותר; some more= עוד;
(I also wrote יותר, and think it could be accepted).
ani khoshev sh-anakhnu tzrikhim leeknot od pastah
If the person saying the sentence is a male (since it's חושב) - how could it be אנחנו צריכות ?
You are right, it is a weird sentence.
Yes, there is not gender congruency.
This is a perfectly acceptable sentence. If there are a group of us in a restaurant, it would be quite common for one of the group (I think) to say to the others WE should order more of something, e.g. עוד יין
I translated this sentence from English like: "אני חושבת שאנחנו צריכים לקנות יותר פסתה" Might it be correct too? Please advice!
Yes, it works too. (Except the spelling is פסטה with a 'ט).
יותר פסטה should be accepted
How do you know if it is a male or a female speaking? It only says "I"