Short, direct answers:

1. Can abhavya (abhavi) jīva do granthibhed (grantibhed)?

No. - Granthibhed = breaking the deep knot of mithyātva-mohanīya karma, through which samyak darshan (samyaktva) arises. - Only a bhavya jīva (one who is capable of moksha) can do this. - Abhavya jīva is defined as a soul that will never attain samyak darshan or moksha in all three times (past–present–future). - So abhavya jīva can never reach the inner state required for true granthibhed.

1. Can abhavya jīva “touch” samyaktva (even for a moment)?

No. - By definition, abhavya means: a soul that will never get samyak darshan, and therefore will never go on the path of liberation. - Samyaktva is the first real step of moksha-marg (4th guṇasthān), so a jīva who is forever unfit for moksha can never even momentarily attain real samyaktva.

Summary:

• Bhavya jīva – can have granthibhed, can get samyaktva, can ultimately get moksha.
• Abhavya jīva – can never have granthibhed, never get samyaktva, never get moksha.

You can read a simple explanation of bhavya and abhavya jīva here: