Preparation of an aromatic Grignard reagent I was tasked with preparing 4-fluorophenylmagnesium chloride from the corresponding aryl chloride. But I've heard that aryl Grignard reagents are very difficult to prepare. I think that the optimal solvent for the reaction would be THF. Any advice would be greatly appreciated!

Also what are the downsides of using magnesium powder instead of magnesium turnings?
I have prepared many aryl Grignards in my career. Generally the aryl bromide or iodide is easier than the chloride, but it can be done. THF is certainly fine for this, run under inert atmosphere, of course. Magnesium powder may prove to have more of an oxide film than turnings and hence be less reactive. Most Grignard preps use turnings. It might be helpful to give your $\ce{Mg}$ turnings a brief wash with $\pu{2N}$ $\ce{HCl}$, then rinse with $\ce{EtOH}$ and $\ce{Et2O}$ just before you use them.

To initiate the reaction - do not stir the reaction but either hotspot it by using a heatgun to heat the region immediately around where the turnings sit at the bottom of the flask or put the whole flask in an ultrasound bath. A crystal of iodine in the reaction mixture will often serve to initiate the reaction, when it decolourises you know the reaction is proceeding. Depending on scale the heat of the reaction may bring the solution to reflux so you'll need a condenser on it.

Finally if all else fails at couple of mls of Red-$\ce{Al}$-$\ce{H}$ solution should start it. 

If all fails with $\ce{Mg}$ metal, consider running a Knochel exchange with $\ce{iPrMgCl}$.