"If I were to get some more yeast is it ok to put the yeast in the same starter or make a new one?"
well you dont know if thats contamanted or not,
how did you steralize the wort before adding the yeast
bactera in there will make a cloudly mass at the bottom as well
the best way to do what you are trying to do is with agar and a petri dish
its really not hard and you can make sure you are just growing yeast.
there is tons of information out there on this , just look on mushroom growing sites
there method is the same in every regard ,yeast and mushroom micilla both love malt-agar.
if you do it this way you can take a cuture from anything and isolate it and make all the starters you want
you can get presteralized agar and dishes