some people say allegro is 120-160 and some say it is 120-130.

I agree with the 120-160 for these reasons:
1) not all allegros are the same and so all those different allegros should all be in the allegro range
2) If 140-160 which is molto allegro was not in the allegro range it would be considered Vivace and Vivace pops up much less often than Molto Allegro does.

Some people say andantino is faster than andante and that andante moderato is slower than andante. I disagree with those that say that for these reasons:
1) I was always taught that it was the reverse with andantino being the slower one and andante moderato being the faster one.
2) Just because allegro moderato is slower than allegro does not mean the same thing is true for andante and andante moderato.
3) -tino when applied to tempo means slower than
4) the moderato part of andante moderato tells you it is closer to moderato just like it does with allegro moderato.