Let me add a couple of points.
Question 1: in my experience, ASW spread always refers to the spread between a particular Bond and the IRS of the same currency. Most commonly, this would be a spread between government bond and the corresponding IRS.
In a par-par ASW, you trade a fixed notional (say 500 million USD), whereby you swap the fixed cash-flow on the bond for a floating rate + spread, where the spread is referred to as the "Asset-Swap-Spread".
Imagine a USD bond trades at par (so the bond coupons correspond to the bond yield). If the coupons are semi-annual, then the coupon payments also exactly correspond (timing-wise) to the fixed coupon frequency of a USD IRS (which trades as quarterly float vs. semiannual fixed).
If the bond coupons are greater than the fixed rate on the IRS, then the ASW spread is positive. If they are smaller, the ASW spread is negative. Whenever the ASW spread gets less positive (or more negative, if it's already negative), this is referred to as "Asset Swap Spread tightening". Whenever the ASW spread gets more positive (or less negative, if it's already negative), this is referred to as Asset Swap Spread widening.
(If the bond doesn't trade at par, it works the same way, you essentially swap the bond yield for the fixed IRS rate + spread).
Credit vs. ASW spread: in my experience, government bonds, even emerging market bonds, mainly trade as an IRS instrument, not a credit instrument. For example, all European govies have some "credit spread" on the German Bunds, but (except for Greek bonds, which used to be driven by credit), all of these European govies trade as an interest rate instrument linked to the corresponding central bank policy rate (and other factors, such as demand by funds & local insurance companies, etc). To my knowledge, very few people (if anyone at all) trades credit in European govies (for example, taking EM markets as an example again: the Polish or Czech credit default swaps are pretty illiquid, and the credit component of the bond can thus not be traded in a meaningful way).
On corporate bonds, or Latam EM govies where I believe the credit component might be more pronounced, what can be traded is the CDS-Bond Basis spread: i.e. the spread between the credit component of the bond yield and the corresponding CDS. This sread can again widen or tighten, but when we talk about ASW spread, we always refer to the spread between bonds and IRS.