“a 1-on-1 native teacher”. You would use "a" if it were '2-on-2,' 3-on-3,' etc; all the numbers. "An" is usually used before words that begin with a vowel (A,E,I,O,U) {an arm, an electric razor, etc). Even though the word "one" does begin with a vowel, the *sound* it makes (sounds like 'wun') is not a vowel-sound beginning. In British English, they seem to include H-words (an + H-word) but don't quote me on that one. ;-)

Yes as Maidhc said above, use an before words beginning with a vowel, and a before words beginning with consonants. The exceptions are with how the words sounds like in the beginning. As he correctly mentioned, one sounds like wun which gives the impression that it begins with a consonant, and hence why you use an 'a'. Another exception would be 'a uniform' because uniform sounds like 'youniform'. Listen out to these sounds at the beginning. Now as for the H-words, this is not fully correct. This is only correct where the H is silent. For example, 'an hour' 'It is an honour' etc. Every other H-word you'd use 'a' such as 'a house' and 'a hat'. Hope this has helped you. :)