Translation:I have not spoken with my friend since Thursday.
I am not a native speaker and I think it may not be totally wrong, grammatically speaking, but it definitely sounds weird to me. When we are talking about basic conversation, whether you are talking to someone or speaking with someone (we use both in English), Spanish uses "hablar con". "Hablar a" seems more to me like "consult".
Why are names of the days of the week preceded with "EL" ie I have not spoken with my friend since THE Friday? Is there a general rule covering the use of EL and presumably LA in circumstances when the word "THE" would not be used in the translation?
I think you just got to learn that fact - always use el with a day. Incidentally if you want to say you did something on Thursday don't translate 'on' just put el jueves. And if youwant to say you it on Thursdays i.e. regularly say los jueves.