Dynamic Quarter Selection

It was using LASTDATE('Asset type'[As_of_date]) In the Current Quarter downloads that was giving you the problem but we also didn't need the filter statement.

Current Quarter = 
VAR _current = FORMAT (  TODAY() ,"yyyy-\Qq" )
RETURN
CALCULATE( SUM ( 'Asset type'[Downloads] ), 'Asset type'[Fiscal_quarter] = _current )

Last Quarter = 
var _last = FORMAT ( EOMONTH( TODAY(), -3 ),"yyyy-\Qq")
RETURN
CALCULATE( SUM ( 'Asset type'[Downloads] ), 'Asset type'[Fiscal_quarter] = _last )

For your second question a couple of notes.

First you should always write a measure rather than just pulling a value into a visual so for downloads we have.

Total Downloads = SUM ( 'Asset type'[Downloads] )

This lets us use that in further measures, prior week for example:

PW Downloads = CALCULATE ( [Total Downloads] , DATEADD ( 'Asset type'[As_of_date] , -7 , DAY ) )

Then we can put them together for a week over week change

WoW downloads = [Total Downloads] - [PW Downloads]

And again for the % change

WoW % Change = DIVIDE ( [WoW downloads], [PW Downloads] )

My updated file is attached for you to take a look at.

If this solves your issues please mark it as the solution. Kudos 👍 are nice too.