Learn English – “I saw you see me”

It, in fact, precisely reflects its meaning! As you read, 'make it up' with someone means to become friendly with someone AGAIN

Check the previous sentence... they weren't talking earlier.

".....thought [sic] we weren’t on speaking terms for our last two years at school."

They weren't on speaking terms means they did not talk to each other for the said period.

The meaning of 'next to' has already been well answered here, but I would like to add in context:

This question introduced me to Einstein's "five houses" riddle which I worked on for an hour and solved 2 days back. Since houses are assumed to be arranged horizontally in the riddle, the Norwegian lives in the first house from left or right and the house 'next to' it is EITHER the house second from left or the (4th) house second from right. Selecting either end apparently does not affect the final question of the puzzle though the exact solution may differ a little.

Note: As pointed out in an earlier answer here, the key with the regular usage of 'first' and 'next to' is not to assume that something is the 'first thing' from the left or that 'next to' means to the right (or left) of something else unless it is specifically mentioned. Otherwise we should proceed with an open mind.

Note 2: a very perceptive answer at ELL did point out the houses could even be arranged in a circle except that the clue 'first' house suggests a linear arrangement.