Hello Marracuen.
1. On the your first Q, you have several threads below.
David, 521AB, Jghrist, Bill, explain it as well as possible.
Punglu also added drw with CT connection.
E/F protection on the Delta side havent any connection to second side.( grounded/earthed it, resistive or ungrounded/unearthed).
Delta side High side see E/F GF fault on the star side only as phase to phase fault, as NPS, but not as E/F ( GF).
and only in case of solid grounded.
1.1. Delta side E/F protection depend on the your system. In case od solid grounded, possible operation of 87T ( diff, of course if it enough sensetive and you have enough fault current) or 50/51 function.
But goodest solution is Punglu drw. simple 51/50N finction with residual connection.
In case of ungrounded system, you need function like to 67N/59N or very sensetive 50/51N--SEF.
2. In IEC land we use term open delta, but on this Forum, we have some agremment, for ANSI land open delta it's something other ( we used term V connection). ANSI land use term broken delta, and we IECland in this Forum try use only
broken delta term ( from time to time we forgot

)
Hope it's help.
Best Regards.
Slava