You could buy Magenta for €19. The version for English speakers is probably best. See http://magenta.gr/index.php/Software/El ... akers.html
I've used it and find it quite good. Not sure if it will help with the alphabet problem? Obviously if you want to look up a Greek word you need to be able to type it in using Greek characters but you don't need to know which order they appear in the Greek alphabet. You can also type in the first part of a word and it will give all words with that beginning. It's quite good at showing different meanings of the same word. It also tends to show the nominative plural of nouns as well as singular so once you know the structure of Greek endings you know which pattern it follows. Similarly for adjectives it will show the masculine, feminine and neuter endings so again you can know which pattern it follows.
PS My wife went to the trouble of writing the alphabet down the right had column every few pages in our dictionary so you could always find it whatever word you were looking up.
PPS Magenta is also available as an ap for iPhone/iPod/iPad devices through itunes for only £2.49. See https://itunes.apple.com/gb/app/magenta ... 21466?mt=8
I can't find exactly the one for English speakers as an Android ap but the Greek version is available together with various other free ones, see https://play.google.com/store/apps/deta ... glishgreek
Since they are free it doesn't cost anything to try them if you have an Android device.