Regarding the second question, you can go directly to Wiktionary, and type there
http://de.wiktionary.org/wiki/[Your prefix-]
(for instance, for über, type http://de.wiktionary.org/wiki/über- and you'll find out, it's both trennbar and untrennbar, as you already know from your example.)
As you already realized, a direct search for the verb gives also a list in Wiktionary. It's also interesting the search in dict.cc, where you can type [Your prefix*] or [*your sufix / root verb]
Example:
- Say you are interested in all verbs with prefix miss. You just type
http://www.dict.cc/?s=miss*
That renders too much noise. But you know verbs end in-en, so you better search
http://www.dict.cc/?s=miss*en (as everybody knows, * stands for anything)
- You are interested in the verbs having the form
[Prefix]-sprechen. You just invert the search:
`http://www.dict.cc/?s=*sprechen`or to perform a more restrictive search for, say, a 3-letters prefix, your input would be
http://www.dict.cc/?s=???sprechen