New to Btech so im not up to speed on lore and fluff yet (busting my butt to get there though) but i want to play within its boundaries as much as i can.
No problem. Take your time, and meanwhile, shortcuts like asking here works.
Were there any known Mercenary companies who were Very Loyal and exclusive to one house that could almost be counted as a member of said houses military?
Numerous. In some cases, they end up totally absorbed by the "client". A prominent example of that is the McCarron's Armored Cavalry unit (also one of the larger ones) as well as several other units among the Citizen's Honored of House Liao.
Other examples include the Gray Death Legion (Steiner) and the New Avalon Cavaliers (Davion)
Those are all quite sizable, it's possible that some exist at the Company level without being specifically mentioned in canon; at some point it goes beyond the intended scope of books to record every mercenary unit unless they're prominent in some way.
Also would it be outside of fluff for a houses Military company to function far outside that houses borders on their own almost like a mercenary unit, requiring themselves to use salvage to stay operational for extended periods of time until back in contact with their respective houses?
It happens, but it's rare. The most prominent example that comes to mind is McCarron's Deep Raid, but I could see it happening at a much smaller scale. Operation Bird Dog, preceding Operation Bulldog could be an example of that.
The key question to answer is: why bother? What advantage is gained by putting a company of Mechs at such risk of failure just by being beyond their usual supply lines? That question can have many answers, just make sure it's a cool one and you have the premise for an interesting campaign.
Paul