Avalanche puts every spare pound or dollar against the highest interest rate first, which always costs the least in total. Snowball puts it against the smallest balance first, which clears the first account soonest. This page simulates both and shows the gap, because the right answer depends on whether the saving or the early win is what keeps you going.
The monthly budget is every minimum payment added together plus whatever extra you commit, and it stays the same size throughout. When one debt clears, its minimum is not pocketed: it moves onto the next debt in the order. That is why the last debts fall much faster than the first.
Because the budget is not out-running the interest. If the interest charged in a month is more than the payments made, the balance grows no matter how long you keep going. The page says so rather than showing a date that cannot happen. Raising the extra payment is what fixes it.
Consolidation replaces several debts with one, usually at a lower rate. It helps when the new rate really is lower and the fees are small, and it hurts when the term stretches out far enough that the total interest rises. Work out the new loan on the loan calculator and compare the total against the figure here.
Whatever the account requires each month to stay in good standing. On a credit card it is often a percentage of the balance, so it falls as the balance does. This page holds each minimum steady, which is the conservative reading: a falling minimum would drag the payoff date later, not earlier.
A plan is easier to hold to when you can see it working. Aventurine tracks balances, categorises spending and charts the trend, in an encrypted file on your own machine.