2. The senate passing it makes no difference. The Republicans, controlling the House and the Senate, may well have been successfully in passing legislation withdrawing from the treaty. Except - that isn't even necessary. Trump can withdraw from any treaty he likes whenever it pleases him: https://www.washingtonpost.com/news/monkey-cage/wp/2018/05/0...
All of these are simply internal American processes, and it is up to the Americans to consider wether they want their politicians to run a foreign policy that projects stability, where the decisions of previous presidents are maintained because, being legitimately elected it was their decision to make, and American's word should stand for something - or whether they want their country to be perceived as erratic - which is in fact the case now, whether or not it causes allies such as the EU to ultimately make real changes in the relationship.