On the first question you'll want to use authentication for sending mail since you'll be coming from the outside when on 3G. Does that server even allow SMTP from the public side? If it does than most likely requires authentication. Or depending on your provider they might be blocking SMTP as do many ISPs but for me that isn't the case.

 

I have an imap account set up in K9 mail and I used 25 for the outgoing port. A friend of mine has an iPhone and has a different outgoing port that works for her phone. Maybe try 25 and see what happens.

 

Originally I had the same problem an alert kept popping up about incoming and outgoing servers not functioning.

What you have to do is use the incoming and outgoing servers you posted earlier, which are correct. Hit the drop box while setting up incoming mail, the one that says POP... switch it to IMAP fill in the rest of the requested information and proceed to advanced settings.

Make sure both incoming and outgoing servers are set to SSL and automatic.

Worked for me not sure how it affects the email account on drexel one since its SSL on the android.

 

I encountered this exact same issue. Everything works great, just can't send SMTP outgoing email unless I'm on wifi.
Sadly, I ultimately ran out of patience and ended up requesting or establishing wifi networks nearly everywhere I typically end up. This "solved" the problem in reality but I technically never solved it. I believe it to be a port issue. It might be solved by requesting that my hosting company allow SMTP on different ports so that I could troubleshoot this. Again, I ran out of time & patience. OP, hopefully you have more luck.

 

Maildroid.
Problem solved.