What IFR clearances may a pilot obtain from ATC directly without a pre-filed flight plan with FSS?
The theoretical answer to your question is that you can always get an IFR clearance directly from ATC over the radio, and filing a flight plan in advance isn't required (but it is strongly advised to avoid delays).

In reality, however, you should file in advance if at all possible. This is from the AIM 5-1-8 (my emphasis):


  Instrument flight plans may be submitted to the nearest FSS or ATCT
  either in person or by telephone (or by radio if no other means are
  available). Pilots should file IFR flight plans at least 30 minutes
  prior to estimated time of departure to preclude possible delay in
  receiving a departure clearance from ATC.


The IFR flight plan system is there for good reasons: it helps ATC manage busy airspace and it avoids the need for lengthy radio discussions. If you don't file a flight plan in advance then you'll probably annoy ATC and you may be delayed because they can't take your request directly.

Pop-up clearances by definition don't have a full flight plan filed in advance, but they do have an abbreviated IFR flight plan:


  An authorization by ATC requiring pilots to submit only that
  information needed for the purpose of ATC. It includes only a small
  portion of the usual IFR flight plan information. In certain
  instances, this may be only aircraft identification, location, and
  pilot request. Other information may be requested if needed by ATC for
  separation/control purposes. It is frequently used by aircraft which
  are airborne and desire an instrument approach or by aircraft which
  are on the ground and desire a climb to VFR-on-top.


Weather isn't predictable and a VFR flight may have to become IFR for safety reasons, so there needs to be some flexibility for aircraft that are actually in the air. A pop-up clearance is just a different, simpler way of requesting an IFR clearance; once you have it, you're IFR and operating in exactly the same way that you would if you had filed in advance.

Descending to VFR conditions is an interesting idea but ATC can't clear you to descend below the minimum IFR altitude for the area. You could request the lowest altitude ATC can give you, then cancel IFR if you break out. But descending without a specific altitude restriction seems very risky: the temptation would be to keep going lower to "have a look", and that could end up as a CFIT incident.

Finally, at least in my experience the 30-minute 'rule' is really a guideline to avoid delays. I've never had an issue filing IFR and departing 15 minutes later, but then I'm usually flying between class C or D airports and the airspace isn't particularly busy. A class B airport is probably a different story.