Putting Together

I used the internet to make this, so you can use it too. But only use it where you need it,
and if you don't have free access to the internet you can figure out as much as you can alone.

This puzzle has several parts. The parts are:
Iterated addition 1
Animal families
People liked that, so let's do it twice
Through lands and oceans
Largest
{TODO: make and add puzzle}
{TODO: make and add puzzle}
Keypad runes
Iterated addition 2

The five-line section between braces is not part of any of the sections, but it is helpful.

Iterated addition 1: metal 2

0 1 -> 1
0 2 -> 0
0 5 -> 2
1 0 -> 0
1 7 -> 13
2 6 -> 13
3 7 -> ???

Animal families: space 1

Look at the diagonal.

Electric eel
Red panda
Two-toed sloth
California condor
Pig-nosed turtle

People liked that, so let's do it twice: gas 1

A grassy area in a college campus
A technique that can be used to make a shape
A type of spell (What is this one doing here?)
A type of cephalopod
Making all the different parts of something into one
Reflectional symmetry
Removing or destroying a large part of something
The month when school usually starts
The most common type of star
The name of the shape being made
The other possible name of the shape being made

Through lands and oceans: space 1

Start in the capital of Japan, which is on the coast of the Pacific Ocean.
Go 3,859 miles, to a place which is on the coast of the Pacific Ocean.
Go 8,547 miles, to a place which is on the coast of the Atlantic Ocean.
Go 3,341 miles, to a place which is on the coast of the Atlantic Ocean.
Go 5,159 miles, to a place which is on the coast of the Indian Ocean.
Return to where you started, going 8,637 miles.

Largest: space 1

L / (A + R) - G / (E + S + T) = ???
where
L = Largest two-digit triangular number
A = Radius of largest planet in the Solar System in Earth radii (rounded down)
R = Largest even prime
G = Order of largest symmetric group with a nontrivial outer automorphism
E = Largest square Fibonacci number
S = Largest number directly between a square and a cube
T = Largest atomic number of a known element

{
5: I'm just getting tired of writing these puzzles and I want to write a long rambling sentence which (TODO) I have to take out at some point.
6: Actually, something just came to my mind. This might be lunacy, but I'm thinking of going to the extreme and not giving any help at all.
7: Since usually that would make the remaining puzzles impossible, I'll say that the mediocre (unused) options are alliterative.
8: But no, that would make the puzzles too easy. Maybe I could instead say that the second correct answer is in the first.
9: TODO: XXX no good idea found yet, but slight signs of one are coming. Maybe a 68.3% chance or so.
}

{TODO: make and add puzzle}: double space 1

{TODO: make and add puzzle}: double space 2

Keypad runes: gas 1

Telephone, not computer, calculator, or elevator.
13 28 / 13 17 46 79 / 17 19 39

Iterated addition 2: metal 1

0 2 -> 0
0 3 -> 1
0 6 -> 3
1 1 -> 1
1 8 -> 21
2 7 -> 21
3 8 -> ???