I want to know if any body is paralyzed by one hand and one leg and he unable to keep purity and Wudu even he cannot take food by hand so in this case he has to do prayer in time and without Wudu and without purity and he can do the Tazbee in this condition. And one more question at the time of prayer the mind is used to go here and there and some time we use to do the mistake also so in this case it is acceptable prayer or not please reply me as soon as possible.

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.

The Prophet said: “Allah does not accept the prayer of any of you without purification.”

There is a consensus among all Muslim scholars that if somebody is capable of purification, his prayer is not acceptable unless he fulfills the condition of purification.

If a Muslim can perform ablution himself, he should do so; otherwise, he should find somebody to do this for him if possible.
Imam An-Nawawi is quoted as saying: “If a Muslim is unable to perform ablution by himself, then he must find somebody to do this for him either for free or against payment (hired for this job with a reasonable pay). If this is not possible for any reason, then the Muslim should pray in all circumstances as deemed convenient and repeat the prayer later. If a Muslim does not find water for purification or ablution and there was no pure soil or stone for dry ablution (Tayammum), he is to do the prayer in time, but repeat it again when water or pure soil becomes available for use, because the prayer is defective for lack of purification (for a rare case). If a Muslim is capable of performing dry ablution (Tayammum), he should do it.

If your mind is wandering here and there during the whole or part of the prayer, it is valid apparently as long as it fulfills all the prerequisites of the prayer. This means that the Muslim does not need to repeat the prayer if he does it with absence of mind, but he gets no reward for the part in which he is absent minded during the prayer.

For more benefit that Tayammum is impermissible if water is available, please refer to Fataawa 357823, 106625, and 84036.

For more benefit on Tayammum, please refer to Fataawa 241396, 88999, 237019, 92216, and 91484.

For more benefit on how to perform Tayammum, please refer to Fatwa 85128.

Allah knows best.