The Embrace The Shadows Orpheus Solo Mode enables a SM to ignore the -30 penalty from their Power Armour to Concealment and Silent Move Tests against Tyranids.

Does this count for all Power Armour incl. Terminator and Artificer or only Astartes Power Armour?

The Defensive Stance Orpheus Squad Mode Fire by Ranks grants SMs a Full Auto Burst action with 2 hits per Degree of Success instead of 1.

What about a Storm Bolter with the old (put up to now official) weapon stats? Do you get 3 or 4 hits per Degree of Success?

All the GM bones in my body (three of my digits, two metatarsals, 5 vertebrae, and my right clavicle) are screaming at the idea of ever allowing a player to ignore stealth penalties for Terminator Armor. Additionally, one could argue that Power Armor and Terminator Armor are quite distinct. Artificer armor, on the other hand, I'd allow, given that it is Power Armor that is super fancy.

Fire by Ranks states that the hits are limited by the weapon's Rate of Fire. The ability simply makes it twice as easy to get the maximum number of hits in. So yes, a Storm Bolter would be racking up several hits per... hit, but only up to its normal maximum of 8 hits.

I'm not quite sure because Terminator and Astartes Power Armour get their penalty from a general rule concerning all Armour with an AP of 7 or more. Terminator Armour get their own penalty for subtracting -20 from Agility. So a Terminator normally gets a -50 penalty to Silent Move and Concealment and an additional -10 to Concealment from Hulking when moving.

From what I understand this Solo Mode is more linked to exploiting tyranid sensory weaknesses than to moving cautiously unlike the Raven Guard Guerilla Training Talent.

Stealth Terminators are a possibility. The Horus Heresy novel Legion does show Alpha Legion with a unique squad of first company Terminators that are infiltration specialists. These infiltrator TDA suits feature near silent running, they don't set off motion, tremor, IR, or other electronic detection devices, and are seemingly unique to Alpha Legion.

I'm pretty sure, with it specifically stating "Power Armor", that it only intends to be used with Power armor (and its variants). Terminator armor is NOT power armor. The two are not even closely related.