A Hawley retaineris made of stainless steel wire that forms the bow that wraps around the front teeth and the clasps in the back. The plastic part is acrylic madefrom Moving acrylic liquid monomer with acrylic powder. What you are probably tasting is excess liquid monomer from the fabrication of the retainer and is normal. It should go away with time or you can soak it in denture cleaner found at any drugstore. Concerning the rough spots I suggest going back to see your orthodontist so he/she can smooth it out.
Based on the photos provided it looks like it will be necessary to remove teeth in order to gain the space needed to align the lower front teeth. However, extraction of four bicuspids may not be the only option. I would reccommed going back to see your orthodontist to discuss the possibilty of removing only one lower incisor to gain the sapce needed.
It sounds like you may have a low Maxillary labial frenum, which is the muscle that attaches your lip to your gums. The pulling force from this muscle can cause space between the front teeth to open. If so I would recommend you go back to you orthodontist to tighten the retainer which can close the gap (if it is small enough). Once the gap is closed I would then recommend having the orthodontist place a permanent retainer on the back of the two front teeth to prevent space from opening up again. It is also recommended that you see a periodontist to have a frenectomy performed which will eliminate the pulling force from the muscle.
Based on the photos you posted it does look like you are in Class I Occlusion. The space that you see between the top and bottom teeth is very common with orthodontic treatment. There is typically a "settling in" period after braces are removed, which takes approximately 3 months. During this period the teeth come tother and the space closes. Your bite will look better after the sttleing is complete..
Current research shows that extraction of your wisdom teeth alone won't prevent relapse post orthodontic treatment. Proper retainer wear is the only way to ensure stablity of the teeth. That being said, you have various options to correct your smile depending on the results desired. Your best bet is to go see a local orthodontist for a consultation to discuss these options (consultations are usually free). I would also recommend seeing your general dentist because in the photo it looks like you have a "black traingle" between your top two front teeth which can sometimes be an indication of periodontal disease.