It is perfectly normal to see the odd thread rearing its head from the end of a seam. This is simply excess thread at the end of the stitch where it has been tied off in production.
If you’re concerned about its appearance, any extra thread can be trimmed down carefully with scissors.
To tighten Chest Zip Suits you only need to pull the 'longer' side of the elastic. The 'shorter' end (that is stitched to the front of the suit) doesn't really tighten.
If you plan on using your suit every day for a week, then don’t need to worry about being too thorough every day. Just rinse it in some cold fresh water, getting rid of salt and sand for use tomorrow. Oh, and try to dry it if you can – there's not much worse than putting on a cold, damp wetsuit.
Whatever you do, don't tumble dry the wetsuit.