かい、まい、だい are音読み<おんよみ onyomi>, so you should use いち・に・さん・し・ご・ろく・しち・はち・きゅう・じゅう（おんよみ）before them basically. Nowadays, we often use よん and なな instead of し and しち to avoid misunderstanding among "いち" and "し" and "しち". 　 いっかい・にかい・さんがい・よんかい・ごかい・ろっかい・ななかい・はっかい／はちかい・きゅうかい・じゅっかい

I think the Japanese counters are difficult to learn but please get accustomed to them little by little. The answers are: いちだい、にだい、さんだい / いちまい、にまい、さんまい / いっかい、にかい、さんかい *ふたつ already includs counter which is つ, so "number + counter + counter" doesn't exist. one car, two cars, three cars --> いちだいのくるま、にだいのくるま、さんだいのくるま one sheet of paper, two sheets of paper, three sheets of paper --> いちまいのかみ、にまいのかみ、さんまいのかみ once, twice, three times --> いっかい、にかい、さんかい *the first floor, the second floor, the third floor --> いっかい、にかい、さんがい I hope this helps you. Good luck!