If the e-mail has been signed with a first name only, then that indicates that the writer is happy to be addressed by his/her first name. But many students would feel more comfortable using 'Dr X' and nobody could take offence at that either!
I'm a university academic by the way. Some of my (uni) students use my first name immediately, a few never do.
As the others say, if the person signs with their first name, reply to it.
Most academics don't use the Dr title that much in everyday life, it's generally first name terms all round in the institutions I've worked in (not like my undergrad days when the tutors used to call me Miss Surname, as if we were in a Victorian novel).
If you have a reply with a first name signature, fine. For a first contact, I'd keep it formal and go for Dear Dr X.
I work in a university and get emails sent to our departmental email address. Some potential students use this to send enquiries about a course. They know from the prospectus the name of the academic in charge of the course - let's call her Mary Smith. I am old-fashioned, not to say stodgy, and I find it quite surprising how many of these emails are on these lines:
hi mary ur cours looks gr8 can u send info thx Luce x
and when you look at the email address it's something like sparklypinkmermaid@...
It's a vocational course. It should be very obvious from all the marketing material we're looking for people with a very professional attitude. None of the above makes a good first impression!
I've just got back from running a meeting in the US where one of the delegates said 'one thing I like about working with the english is they call us all Professor!' apparently it doesnt happen in the US!
Hi London Mother and OP. I think if the OP has in her hand an email signed with a first name then she can proceed like this: Dear Sieglinde (if I may) and sign with her own Xtian name. if not, it's 'Dear Professor Walsung', or 'Dear Dr Walsung'. No point in alienating people. That said, I wouldn't be alienated myself. It's worth googling to see which of the above she is.
OT elastamum - i suppose there is a different system of titles and way of addressing people in different countries. i also noticed some of the exchange students /we get some americans amongst other nationalities/ address all the teachers with ' professor'. in my country a professor is the highest academic title you can get and comes after a doctor and a docent/associate professor. so only a few of the teachers on the highest posts are professors.