Here's some info about how the vids were shot, including equipment, cables, adapters, etc. It's really straight forward:
http://keith.tristesse.com/page/about_videos
"Cleared direct Willey Post Airport, climb and maintain 4000" gives you what you need. If you're heading the other way at the time and he needs you to turn for traffic or because he's running out of airspace, the next you think might hear is "fly hdg xxx, proceed direct Wiley Post when able," but you shouldn't expect to hear that every time. You're fine without it, you would just dial GPS direct to that airport (he won't issue direct if you don't have RNAV capability, or shouldn't at least. If he does...and you don't have it, then you can say, "unable, we're /A" or /U).
Regarding the fact that he cleared you to an airport other than the one you wanted, don't let that rattle you. It can be tough for them to keep track of the fields you want to go to when shooting lots of approaches (approach TRAINING is pretty far removed from real world IFR flying in that regard) at different fields. No worries, though, just say, "negative, we need IFR to Page."
Any time ATC gives you something other than what you need, don't be alarmed. It doesn't always mean you can't have it or you'll be in trouble for asking for something else. Just politely ask for what you need and see what happens. In the case of a clearance limit being wrong, that's going to get fixed 100% of the time. Now, if he clears you there via a route you weren't expecting and you want direct, you can ask, but in those cases, don't be shocked if he says no.
Picking up a clearance in the air is not much different than doing it on the ground, other than the fact that you're already radar identified, so you're not going to get a new squawk (typically). In your case, you were getting a clearance limit and route all in one phrase, "cleared direct Wiley Post." If the routing was more interesting, it would've been "Cleared to Wiley Post via [full route clearance, whatever it is], maintain 4000"
When you ask about switching from VFR to IFR...you said, "say you were filed for a long VFR flight..." and I'm going to stop you right there. That you have filed a VFR flight plan doesn't matter....at all....to anyone....ever.....except Flight Service. So, let's take that out of the picture and start again
Let's change it to, "I'm on a long VFR flight and I'm receiving advisories from ATC..." and now you want to swap to IFR. It's absolutely appropriate and can go one of 3 ways, from easiest to hardest. I've hit at 3, btw, and they are:
1) "sure....cleared to [destination] via [route] maintain [altitude]"
2) or, "verify you're instrument rated and the plane is certificated for instrument flight" "Affirmative" "Great, for the tapes, say first and last name, address, fuel and souls." (something along those lines). You read it back, quickly (they're not listening, they just need it on tapes if you go down), then you get the spiel from DOOR #1.
3) "unable, contact Flight Service, file with them and call me back." (which is a pain in the air, but doable)
I've had #3 happen precisely once. Truthfully, I don't think you're likely to see #3 very often (if anyone else has had it happen, post here and share the circumstances, please!). In that case, it was a training environment and the guy wanted to prove a point that if you're going to do anything other than local approaches, you might want to have a flight plan filed back to your final destination if it's outside of the facility. In my case, I had filed from Allentown to Lincoln Park, shot a bunch o' approaches at Allentown, then asked for a clearance back to Lincoln Park (literally 15 mins away, but still a different facility), and was told #3. The instructor I was with said he'd never heard it in several years of flying. No matter, I filed with FSS in the air, it was good experience. I have a kneeboard (that I don't use) which has a plate on the front showing a few key pieces of info...and one is the elements of a flight plan, so you can read it in the correct order to ATC or Flight Service. I've had to use it a couple of times.
And lastly, yes, you can practice this on PE, absolutely...just pick up flight following and then at some point, ask for IFR. I do it all the time for practice here. Expect Door #1 if you're just asking for a short range IFR clearance. If you need something much longer and it isn't covered by a TEC route, they might ask what route you had in mind.
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