Brenda,
I'd say that the best bet would be to catch BPB first at 5:15 and then head over to Aladdin. Reason being is that Aladdin is 45 minutes long, so you definately wouldnt make the beginning of BPB. The BPB stops are usually 15 minutes a piece so you should be done seeing the entire stop at 5:30 if you catch the parade at the first "party zone" . BUT! There are 3 stops...so if you want to catch the last stop...you should be able to catch the 4:20 Aladdin. The stops generally last about 15 minutes each. So, you would figure that the BPB would hit the last "party zone" at about 5:45, giving you plenty of time to make it. I hope I'm not making things more confusing...
Basically, all 3 stops are the same...so you just need to catch one 15 minute stop. So, you can hit the first zone, get done at 5:30 ish and head over to Aladdin to catch at 6:05. OR...you can see Aladdin at 4:20 and hit the last party zone at about 5:45. So, you do have options!
As far as catching the Toy Story section, you will want to be at the very end of the party zone since the Toy Story floats are the first ones. The parade travels through the whole party zone before stopping.
And for your last question, DCA doesnt get crazy busy during this parade, its nothing compared to Fantasmic or Remember in DL. It is nice to find a good spot to where you dont have to jump over people to see. Keep in mind though that you will probably be standing up anyways, because they have you dancing and moving around. I would say you could grab a good spot anywhere from 15 to 20 minutes before the show.
OH! And one more thing...on really, really hot days, the BPB only makes one stop at the first "party zone"! So, keep that in mind if you decide to go w/ the 4:20 Aladdin show.