transistion from crate to house training + odd poop Q

Did he have coccidia? My puppy had that when I got him and did have diarrhea off and on. Just follow through the course of meds as directed, when they're finished bring in another stool sample and recheck for parasites. If the diarrhea is still happening once he's clear for parasites, you'd want to look into other possible causes... but for now it's probably safe to assume it has to do with the coccidia. Coccidia meds do not kill the parasite, what they do is stop it from reproducing and allow the puppy's immune system to finish the job.
 
I'm not exactly sure what you mean by "facilitating the transition" (to what?), maybe you want to elaborate a little more on what your questions are.... "Crate training" just by itself means you're getting the dog accustomed to being crated so that when he's in there he's calm and comfortable. Crate training in conjunction with housetraining means you're using the crate to help prevent accidents. If you have a crate trained dog, you'll always want to use it periodically so he stays comfortable with the crate in case you ever need it. Once your dog is totally housetrained - usually around 6mo or so if you started early - you may only use the crate to confine him when you leave the house so that he won't chew things. Once he's more mature, he may not have to be crated when you leave, but maybe he still sleeps in there - but that's probably not until he's 18mo old or so.

I would say coccidia is probably what you are thinking of. Did they give the dog med? My dogs has something similar recently and while they couldnt see much under the microscope, they prescribed a few meds that would knock out both parasites and anything else.. If the diahrea worsens, my advice would be the same as the vet. My vet suggested I fast the dogs (both my little puppy and adult dog) for 24 hours and then switch to a bland meal (boiled chicken and rice 2 parts rice/1 chicken) In fact the suggested this PRIOR to doing meds and an exam as sometimes they just have an upset tummy.  Although it didnt improve, its best to feed a bland diet until they are better, even if meds are necessary. So we took our meds until they were gone, and ate our chicken and rice and VOILA...all better!

Well it seems like it was a one time thing, not runny stool for a number of potty breaks.  Yes coccidia is what it was, and yes they gave me medicine for him. 
 
About what I mean by transition from crate to house training, is by letting have more space than just his crate when I'm gone, (e.g. a playpen thing attached to his crate or leaving him a designated room). Hes only 10 weeks at most now, so  I know i have at least a few more weeks until I will come to that point. I just want to know when the time comes. I just want him to have the option to romp around a little bit more than he can when hes in his crate if he feels like it when I'm out of the house for a couple hours is all.