Unfortunately, point 1 has been a persistent problem since parameters were introduced but being lists, are also quite limited in their functionality. The great news is that this has been part-rectified, the not so great news is, that this only applies to 2018.2 and the use of extensions (Tableau Extension Gallery (BETA) )
As an alternate, one parameterised function I pulled together a while ago that might work for you involves a switch between the Max(Date) field so for you, filter your year to Max(Year) and Week to Max(Datepart('week',<Your date field>)) and then use the parameter simply to switch between using the maximums, which will always be the latest periods in your data, or a selected value from your pre-populated parameter.
As for your second point, I am lost as to the problem if you could explain a little more:
It sounds as though you are saying that by using a parameter to determine the period, you are then actually seeing just the last week, but manually updating the url is then preventing the date of the second workbook from being altered. Please can you confirm this and, how you are applying the url value as my previous use of parameters in this way (I regularly use this method), has not created the problem you appear to be describing.
thank you for your answer.
Concerning point 1: I will try the Max values.
Regarding point 2:
The situation is as follows: On the dashboard, you can select the week with the Week parameter and the year with the Year parameter. When I publish the dashboard to Teableau Server, you can use the URL to send values for the two parameters, e.g. Year=2018 and Week=42 (i.e. //&Year=2018&Week=42). When I do this, the dashboard is set and called for the corresponding week. However, the parameter also calculates a filter that represents the last 6 weeks. This doesn't work anymore and only the one week from the URL is displayed in the corresponding area. Furthermore the user can't select another week, the dashboard remains empty, because the 42 as week remains part of the URL. This is not a nice behaviour ...
Thanks and greetings