1) market convention is that the bond buyer pays the accrued interest to the seller...and that is reflected in the "dirty price"

2) sortof. if a bond price goes up, its yield gos down. this is correct.

However, spread to benchmark depends on the "relative" yield change vs the change of the benchmark yield. If your bond yield goes down 5 basis points...and the benchmark yield goes down 6 basis points...then your bond did not keep up with the benchmark, and so the spread widened. See, its all relative?

just google it...you're welcome
 

I'd like to add one point in question 2. Basically its true bond price goes up with yield going down. But I do think we need to care about the time period we talk about. Let's say at time t, yield is lower than coupon so bond trade at a premium. If we are talking about yield going down the very next day, then yeah, bond price goes up. But let's say maybe yield goes lower ONE YEAR LATER, price may end up lower because of coupon payment.

 
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just google it...you're welcome

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