Are there any things one can do which would prevent Allah from accepting their duas?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Allah commanded us to supplicate Him, and He promised us to answer our supplications, but there may be obstacles from the supplicator that prevent his supplication from being answered, such as supplicating for a sin, or severing the ties of kinship, or other characteristics that may prevent his supplication from being answered, such as consuming what is unlawful.

The Prophet mentioned: “…A man who travels a long distance with his hair disheveled and covered in dust, then he raises his hand towards the sky (and supplicates Allah), 'O Lord, O Lord,' while his food is unlawful, his drink is unlawful, and his clothes are unlawful and his nourishment is unlawful. How then would his supplication be accepted?” [Muslim]

This means that it is most unlikely that his supplication will be responded to because his food, drink, and clothing are forbidden.

The same thing applies to hastening the answer, as this is one of the impediments that prevent the supplications being answered.

The Prophet said: “The supplication of a person is answered as long as he/she does not supplicate for a sin, or for the cutting of relations with kinship, or does not become impatient. It was said: “O Prophet of Allah! What does ‘become impatient’ imply? He replied: “It is when he says: 'I supplicated, and I supplicated but my supplication was not answered. Then he becomes frustrated (in such circumstances) and abandons supplication.” [Muslim]

Allah knows best.