Minecraft – How to add scoreboard value to a certain item entity [post 1.13]

There are two things wrong with your command.

1. The target selector for the first execute is wrong, although I assume this to be a typo. It should (probably) be
   @e[score_PigProgress_min=1,score_PigProgress=1]
   although the second part is not really necessary, unless porkchops with a score of 2 are a different thing.

2. /execute does not support matching dataTags, which is what you are attempting in the second execute. You will have to assign a scoreboard value for diamond items, similar to what you did with the porkchops.

Lastly, to achieve what you want, I suggest summoning an invisible Armor Stand to work using the double execute and work from there. I.e.

/execute @e[type=Item,score_PigProgress_min=1] ~ ~ ~ /execute @e[type=Item,score_isDiamond_min=1,r=1] ~ ~ ~ /summon ArmorStand ~ ~ ~ {CustomName:"Marker1",Marker:1b,Invisible:1,Invulnerable:1,NoGravity:1}

This assumes all pork chops and only those have a PigProgress score of 1 or more, and all Diamond Items (and only those) have a isDiamond score of 1 or more.

Now you can execute everything else (/killing the items, saying "Hi", etc.) from the armor stand using

/execute @e[type=ArmorStand,name=Marker1] ~ ~ ~ <command>

Don't forget to kill the armor stand in the end as well.

Yup! What you're doing works just fine, with some minor tweaks.

To apply the attribute modifier to the item, you need to do this instead:

/entitydata @e[type=Item,r=1] {Item:{tag:{AttributeModifiers:[{<attribute stuffs>}]}}}