Is there a problem of "erasing the name of HaShem" if you erase the English word spelled G-o-d, and if so, is there then a problem of erasing it in order to spell it in a more acceptable way (such as G-d), and if so, is there a problem of simply changing the spelling by erasing the 'o' and replacing it with a '-'?
No. There isn't really an issue in writing or erasing 'God'
There is no issue in writing or printing Hashem’s name properly, providing one knows that it won’t be destroyed.
Rambam (Yesodei Hatorah 6:1) writes that there are 7 sheimos (names of Hashem) that mustn’t be erased. There is no issur in erasing a kinui (moniker) such as chanun or rachum, etc. R’ Akiva Eiger (YD 276:9 quoting the Tashbetz) writes that as translations of sheimos have the status of kinuim, there is no issur in erasing them either.
The Shach (YD 179:11) writes that Hashem’s name in a foreign language is not considered sheimos and thus may be erased. Likewise, the Mishna Berura (85:10) writes that the issur only applies to erasing sheimos in Hebrew (See Minchas Chinuch 437:5).
Nonetheless, the Aruch Hashulchan (CM 27:3) urges people to be extra particular when writing letters with sheimos even in a foreign language.
Thus, while it is not strictly forbidden to write or erase the word ‘God’, it is good practice to write ‘G-d’ and such writings must still be treated with respect. Thus, rather than thrown in the bin, a paper containing the word ‘God’ should be recycled with other documents, or wrapped before disposal (See Igros Moshe OC 4:39).