Let's go step by step. It's O.K if you want to make your own "mnemonics" as long as it works for you, but don't attempt to rationalize too much the Spanish language. Why is catorce and not "cuatorce" ? for the same reason that you have "man" and "men" and not "mans". Because each language has its own shapes and peculiarities. In this case because "cuatorce" sound awful. Dieciseis means simply diez y seis. What happen is that in Spanish, the sound "ci" and "zi" are the same, BUT YOU CAN NOT WRITE "zien" but "cien". You only use de "z" for that sound at the end of a word like "diez" perdiz", lápiz" or before strong vowels: a, o and u. Otherwise you use "c" instead of. Therefore, you have "diez y seis·= dieciseis, and the "y" changes to "i" . Rule: In Spanish, you NEVER use the " y" in the middle of a word when the sound is the vowel sound of "i", otherwise, if the sound of the "y" is similar of the "ll" like in "mayo" or "leyendo", it's another thing. Go ahead with your mnemonics, but don't go to far trying to understand the unexplainable.

You'll have to learn the numbers 1-15 "by heart", as my English teacher says. There's no rule... but you can make up rules to remember as you did. An example: From diez (ten) I have to move "once" ;) And then dos-e, tres-e (remember they're with c) The nexts are difficult... "catorce" and "quince" From 16-19 you just have to add "dieci" before the number. (it comes from "diez y" transformed to "dieci") dieci-seis, dieci-siete, dieci-ocho, dieci-nueve. For 20 you have your heart again: "veinte" and maybe for 30: "treinta" The followings to 90 are simpler as adding "enta" at the end. 50 = 5 + enta = cincuenta (o changes to u) 60 = 6 + enta = sesenta (i is lost) 70 = 7 + enta = setenta (i and last is lost) 80 = 8 + enta = ochenta (last is lost) 90 = 9 + enta = noventa (u is lost) For 100 (cien) and latest you have to add "cientos": docientos, trecientos, cuatrocientos, seiscientos, setecientos, ochocientos, novecientos.