1. No conozco a esta (yo utilizaría la, suena mejor) que está hablando con Juan.
In this case, it's something that's going on at that moment...so "esta hablando" is like in English present continues tense...
So, that would be translated as: "I don't know the woman that is talking with Juan.
2. Dile a Emilio que le echo mucho de menos. Dile que me escriba y que regrese a casa pronto.
In this case it's an indirect order, so here we have to use the subjunctive.
Mostly we use subjunctive for: negative command, indirect command (positive or negative), for wishes, for negative opinion, ...
I hope you found it helpful.
If there is anything else I can help you, please, feel free to ask me.
Have a nice day.