I have answers for 1 and 2 below,
Answer 1 - On your dashboard, click on use sheet as filter icon like so,
Answer 2 - Parameters are static, so yes if you're using a date parameter it needs to updated manually. However, with Tableau 2018.2 using Tableau Extensions you can make parameters dynamic. More on this topic here.
Hope this helps.
Ans 1 was so obvious. How could I miss that. Thanks for solution.
Yes solution 2 is a issue though.