All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, we ask Allaah to give you success in finding lawful provisions and avoiding unlawful ones.
As regards developing software programmes that might be sold to companies that deal with forbidden transactions, in principle it is permissible to sell such programmes. Even though these programmes might be used in forbidden ways, the principle does not change nor does the rule to make this forbidden. However, if you know that such programmes will mostly be used in forbidden things, and that they will rarely be used in lawful ways, then it is more appropriate to stop developing such programmes to avoid the harm that is most likely going to happen. The Prophet said: "…Thus, whoever avoids the doubtful, safeguards his religion and honour, but one who engages in the doubtful, falls in the Haram (what is unlawful)." [Al-Bukhari and Muslim]
As regards shaking hands with a marriageable woman, this is forbidden. The ruling and evidences for this are mentioned in Fatwa: 84011, so please refer to it. In order not to embarrass the woman, you could, for instance, hand her a pen or the like when she stretches her arm to shake hands with you, and thereupon inform her that it is forbidden in your religion to shake hands with marriageable women, and that this matter is legislated to protect the society from falling into desires and to prevent all the means that could lead to it. So if you endeavour to do so with sincere intention [for the sake of Allaah] and wisdom, then, Allaah willing, you will overcome this embarrassment.
Concerning killing mice and squirrels to feed the snake, in principle one should not breed snakes as the Prophet ordered us to kill them saying: "Kill snakes." [Al-Bukhari and Muslim] So we are commanded to kill snakes, and breeding them is contrary to this Prophetic narration. Indeed, many jurists stated that it is desirable to kill snakes.
Additionally, one should not kill squirrels, even if it is among the animals with canine teeth, the meat of which we are not allowed to eat. Some jurists stated that it is not permissible to kill that which we do not eat, as this is considered as misuse and Allaah did not order us to kill it.
Imaam At-Tahaawi said: 'It is considered as misuse to kill animals the meat of which we are not allowed to eat, so it is forbidden to do so.' An exception are mice; it is permissible and desirable to kill them, according to some jurists as the Prophet said: "There are five harmful creatures which should be killed even if one is in the state of Ihraam: a snake, a speckled crow, a rat, a voracious dog, and a kite." [Al-Bukhari and Muslim]
Allaah knows best.