I like your idea for an Astro nerf but I don't like adding additional text to core set cards which are meant to be an introduction to the game.
I had an idea for an astroscript nerf whilst still retaining its basic premise was making its text the shorter "If APP is the only agenda in your score area, the advancement requirement of agendas is reduced by 1"
It can still usefully fast advance an agenda but can't astrotrain (and allows lots of clever tricks with agenda forfeiting). Plus the flavour of it being the pilot project and mechanically connected to the SanSan City Grid effect.
Yes, a thousand time yes
I don't think this is going to be enough honestly, its not the link that makes Kate the powerful one.
1 credit extra is not going to outweigh the 20+ credits the Desperado ability gains you. But I don't have the hundreds of playtest games to tell you what an appropriate cost should be
Parasite & Datasucker
I think these are the wrong way round influence wise - its not parasite that's the problem but the ease of reducing ice strength with datasucker. If the latter is too influence expensive for non-anarchs you'll see parasite and the Anarch breakers used as focused 'solutions' (ala Sharpshooter and Deus X) for particular problems in the metagame but they won't form the core rig of shapers or criminals. Having the anarch tools without datasucker will allow for runners to metagame against corps (Komainu too common? slot the parasites!) without being the de facto default rig.
If noise was a mini-faction, who'd be the core set anarch? Maybe make his ability trash viruses to mill, so you can't get the mill and the selling to pawnshop?