Where to start?
First: join the BASC. That gives you liability insurance which the vast majority of land owners will require and you're mad not to have.
The next bit is difficult to word without it sounding patronising, apologies in advance if it seems so, it's not intentional. Even as a beginner you should intend to achieve a kill with every shot. You're right that it isn't possible to guarantee a kill rate of 100%, however, if you're not getting very close to 100% such that a wounding is a very rare event then you should stop shooting live quarry and practice shot placement and range finding until you can.
Pellet choice is a personal thing and what shoots well through my rifle with me shooting, might not work for you. Try a range of pellets in your own gun and choose the ones which perform best for you. Very light or very heavy pellets have their own set of problems regarding trajectory and how much energy they impart to the target - a middleweight (14 to 16 grain) diabolo waisted pellet is a good place to start, Webley Accupells shoot well through my HW35. Heavy pellets at sub 12lbft muzzle energies will have a trajectory like a rainbow at range (great for ratting at 15 yards though!) and lightweight wadcutter target pellets, while they might have a trajectory that's flatter than a Belgian bowling green, will get blown off course by quite mild breezes.
Effective ranges depends on the shooter, not just the gun. Personally I keep 30 yards as my absolute maximum and I prefer to get closer than 30 if possible. I've read posts on airgun forums by people with FAC power .177's and laser range finding gear who kill consistently at 50 yards - but this is extreme, takes a huge amount of practice and is definitely not the usual way of things.
When it comes to permissions, you're going to need patience. You're likely to get a lot more 'No!' answers than 'Yes!". Do get your permission in writing if at all possible - saves a lot of aggravation explaining to your local constabulary if a well meaning passer by calls them about the man in the field with a gun. Likewise carry proof of insurance while shooting.
Excess quarry - I'd wait until you have too many before you decide on what to do with them, Mrs Beeton knew a thing or two more than just recipes
"Don’t take life so serious, son, it ain’t nohow permanent." Walt Kelly