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 animal about which there is an Islamic text that states that one gets a reward for killing it is the gecko.
Abu Hurayrah, may Allah be pleased with him, narrated that the Prophet said, “Whoever kills a gecko with the first blow, a hundred good deeds will be recorded for him; less than that will be recorded for him if he kills it with the second blow, and less will be recorded for him if he kills it with the third blow.” [Muslim]
As regards the lizard, some scholars stated that the lizard and gecko are the same animal, and some other scholars said that they are different and that the lizard is a kind of chameleon.
As for the Salamander, it is a different animal, other than the gecko.
In any case, the animals in the Shariah, in regard to the ruling of killing them, are of four types; As-Suyooti said:
“Animals are of four categories:
1- Animals that are beneficial and there is no harm in them: it is not permissible to kill them.
2- Animals that are harmful and there is no benefit in them: it is desirable to kill them, like the snakes and the Fawaasiq (vicious and harmful creatures).
3- Animals that are beneficial in a way and harmful in another way, such as the hawk and falcon: it is neither desirable nor disliked to kill them.
4- Animals that are neither useful nor harmful, such as worms and beetles: it is neither forbidden nor desirable to kill them.”
For more benefit, please refer to fatwa 342181.
However, many scholars are of the view that the crow that is desirable to kill is the white-bellied crow that eats dead animals – and not all kinds of crows, such as the one that eats plants and the like – contrary to the Maaliki School, who are of the view that all kinds of crows are Fawaasiq.
As for keeping such animals as pets, then, in principle, keeping animals and rearing them is permissible unless there is evidence that they are forbidden to keep, such as a dog that is kept without a valid need.
Az-Zarkashi said in Al-Manthoor, “It is forbidden for a religiously-competent person to keep some things, including: a dog for those who do not need it, as well as the other five Fawaasiq: the kite, the scorpion, the rat, the white-bellied crow, and the snake.”
Accordingly, keeping lizards is subject to the original permissibility, but it is not permissible to buy them, as there is no benefit in them.
The fatwa of the Standing Committee reads, “One of the conditions for the validity of the sale is that the sold item should have a lawful benefit without a need, but the lizards are of no benefit, so it is neither permissible to sell nor to buy them.”
For more benefit, please refer to fatwa 160217.
Allah knows best.