Question 1 - in a sense, TLCs can be used for purity determination. Depending on your method for detecting the spots, TLC can be a very sensitive technique for determining whether there are impurities in your system. After you run your TLC, you just look to see if you have any extra spots.
We actually used this as a semi-quantitative routine purification test at time one for compounds that were being added to our sample bank. A concentrated mixture of the compound in a solvent was spotted in one lane, and the same mixture 20x diluted in another lane. Any impurity spots showing in the concentrated mixture at least as dark as the product spot in the dilute mixture were considered to be a >5% impurity and the compound had to be repurified before submission.
Question 2 - no, once you've fixed your stationary phase in TLC, you've pretty much determined your polarity effect. Basically you have two types - normal phase and reverse phase. Normal phase uses a very polar stationary phase, like silica gel. Consequently, almost any solvent you put with it is non-polar compared to the silica gel, and the more polar your compound is, the more it will be attracted to the plate and the slower it will move. The less polar the test compound is, the further up the plate it will move, regardless of the solvent. (There are some more subtle solvent effects that will occasionally make your spots swap, but not many). So if your product is more polar than the starting material, it will move further up the plate. If you use a more polar solvent, they will both move further up the plate, but the product will still move faster, until if you get the solvent polar enough, they will both run with the solvent front. If you use a less polar solvent, you will move both compounds less, but the product will still move faster, until you are non-polar enough that both stay at the origin. The trick with using all the different solvents is just to get both components moving enough that you can tell them apart.
Reverse phase uses a very non-polar stationary phase, like C18 or C8. These are long-chain hydrocarbons (these two are 18-carbon and 8-carbon chains long, respectively) bonded to silica gel supports - essentially turning the silica gel into balls of grease. Almost all solvents are more polar than the stationary phase. Now, the stationary phase is less attractive to polar compounds than to non-polar compounds, and the more polar your compound is the faster it will run on the plate, regardless of the solvent.