enamel paint = enamel thinner. Mineral Spirits or Naptha. Naptha will speed up drying time. Mineral Spirits likely to slow drying down a bit. ok either way.
lacquer paint = lacquer thinner. and use a good brand at that. you might want to read about "suspension vs. solution" of how lacquer thinners vary. just to know is good.
no other way around it. it may SEEM to work to use non-corresponding thinners, but it's not correct.
to clean stubborn airbrushed, you can use acetone, for any paint. but it is voilatol , nasty stuff, so its up to you. will eat up plastics and rubber, so uhm, play it safe with those materials.