I am a Baal tokea and am trying to learn all the hallochas of shofar blowing. Please provide anything that will help (in English please).

The main issues are:-

1. how to check that a shofar is kosher (I am blowing while covering the other end with my hand to make sure that there are no holes - is there anything else I should do?)

2. defining the notes that they should be correct (I am making my tekiah before and after each teruah: shevarim or shevarim-teruah the same length as the teruah: shevarim or shevarim-terurah )

3. Is there any guidance on the length of the tekiah gadolah?

4. anything else I should know!!

1) besides being cracked, there seems nothing else that would be likely to make the shofar unkosher (assuming that it was not stolen or worshipped as an idol or gold plated or altered it's shape (either by boiling it and making the big side small and the small big or by turning it inside out)
even blowing into it covering the other end to see if there is a hole, in my humble veiw, is not necessary. The Shulchan Aruch
(586:7) holds it's kosher with a hole. Even the Rama who said if you have another shofar it's better to use the one without the hole, the Mishna B'rurah (28) says it's only refering to holes that would alter the sound, but such a small hole that is not detectable thrue sight and only by the above test wouldn't qualify
2) You seem to have that one down well
3) There is no real guidance, the M.B. in 596:1 just says to make it longer than the others. Most people do it untill they are out of breath