First let me say about my last post that I did type it in a hurry so I may have left the impression that everything was very obvious. But the mistake you did I also did many times before the practice made me able to identify better the subjects of sentences. Secondly you did very well when you notice double “et” while I at the beginning totally miss it and only notice it when you point it out. Thanks to you I too discovered the “et…et…” construction that I didn’t know.
My Latin isn’t good enough to analyze your translation but I can answer your question:
amicitia is the singular, why used valemus?Thanks, my friends!
“Amicitia” isn’t the subject of the sentence here, in fact the subject is implied by the verb, and it is us, meaning people in general. “Amicitia” is in Ablative case (don’t know if your book indicates the length of vowels, but if it does the last “a” should be long) and it is being modify by the preposition “sine”. So the last part should translate:
“…but without friendship we aren’t strong and life is nothing.”
Probably “valemus” would be better translated to “be well” but this is a mere guess and nothing I know from Latin.
Best regards and hope this helps,