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Well, there's actually multiple versions of Adamantium... So first you'd have to specify which one you're talking about, the Hulk has broken some versions of it, but they basically mean indestructible by any normal means. So not actually completely indestructible, just might as well be unless you have god like power... https://marvel.fandom.com/wiki/Adamantium https://www.cbr.com/15-characters-who-broke-adamantium/ However, they can all be destroyed with Antarctic Vibranium, which dissolves all metals... While Vibranium can absorb energy, it has its limits and can be destroyed if it absorbs too much energy, too quickly... http://www.marveldirectory.com/miscellaneous/vibranium.htm

The control metal does have a dimensional interlink, which means it can siphon energy from the boost dimension, but as you said the gravity globe does that to a larger extent. actually, we don't know what form that energy takes, but it is probably fairly efficient and the manga or anime has never shown any indications of harmful radioactive effects. it all seems to be pretty safe to be around. since the guyver organism can seemingly change some substances into completely different substances, there is a good chance this organism is capable of spontaneous fission/fusion. loose ions, cosmic rays, etc. would cause damage to the structures and material that it creates, so I imagine it must have a method to manage any excess.

The Control Medal doesn't power the Guyver, its a processor/control system and data storage device. If I remember Correctly the unit siphons a small amount of energy from Boost Space via the Gravity Orb.

I doubt he'd do any better than a normal human would... Unless he is zoa-formed, or acquires a Guyver unit. His extra abilties might make his Zoa-form or Guyver form slightly better than others... But considering we are talking that even scout class Zoanoids are still many times him in strength, speed, senses and resilience over his already superior human traits, he would be done in fairly quickly. Good hits with fancy weapons might allow him to make some kills, sure... but that is still not much better than normal humans could do. The genetic modification of Agent 47's world is nothing compared to the Guyvers at all. Unfortunately, as scientific as the Guyver lore actually is, it is still closer to the edge of science fiction than "science-reality" like in Hitman.

Seeing that the high frequency blades disrupts the surface of any material that it comes in contacts with and breaks it. I can honestly see that the high frequency blades would be able to cut adamantium. It probably won't be able to cut vibranium as that absorbs energy. So the energy produced by the high frequency blades would probably absorbed by the vibranium.

Captain America is at the top of the human limit. Meaning he can match or best any record, unlike those who create the new record has to focus years and years of practice and training to achieve this. And it's all for one aspect of the human body. Meaning a fast 30 MPH runner will not for example be able to run at 30 MPH and lift 800 lbs at the same time. In WG.com it is assumed that when a Guyver is bio boosted, the host's base is Captain America and then 100x boosted.