Sleep

It is narrated from the Prophet Muhammad (S): “Never beat the children if they cry. Fulfill their needs. Because, for the first four months of the life of a child, its cries are a witness to the Existence and Unity of Allah, Almighty." (Bihar al-Anwar)

You should make up the missed prayers and you can also personally ask Allah for forgiveness during du'a.

Yes, actually it is mustahabb to do wudu and recite du'a at prayer times.

However you will not technically be in a state of wudu until after the monthly cycle has passed and you have done ghusl, it is just for spiritual/physical cleansing.
 
However you should not recite the ayat for which sadjah is mandatory and it is said that one should be in a state of purification to recite Du'a al-Mashlool (which you probably aren't reciting before sleeping anyway!). 

I am sorry to hear you went through that. I hope you are not suffering too much on a practical level from your loss. 

As human beings, we are subject to two forces regarding money: the will/sustenance of God, and the free will of human beings.

Sustenance, as something from God, is greater at some times and less at other times. There are times when we receive more than we fairly should, and there are times when we unjustly lose money or other people take it from us (legally or illegally).  In general these things balance out. However, God has promised to sustain everyone, and just because you have lost money now does not mean that it will not come back in some way.

From a human perspective, while one person has the free will to take money from another, that money will not have blessings and that person will probably not enjoy it long term or will lose out in another way. 

Money comes and goes, but what we have is our character and our good deeds. Perhaps the best thing to do is to be grateful that you are a person of good character, you are not a thief or an embezzler, and you are free from the burden of this sin that the other person has committed. You may be anxious now, but thieves never sleep easily!

As for other reasons why it happened.. that is really a matter specific to your situation. Sometimes people take money from us because we are sympathetic, sometimes because we are deceived, sometimes because we are careless, sometimes because they are better at playing games with the law, or other reasons. I am sure you can identify what the reason was and learn whatever lesson you can from it. If your motives for giving money were sympathy or to invest in something positive or something similar, then surely this is something praiseworthy and again you can be at peace knowing that at least you made a good decision.

Beyond that, it is good to spend some time in prayer and ask Allah why this happened. There are many reasons that things happen to us (our own free will, a divine test, part of the divine plan, etc) and perhaps a higher wisdom may become clear. Also, money is often a tool used to push us towards where we should be in life (for instance, needing to go to a certain country or city for work, or needing to leave a place or change our plans in life for financial reasons). 

Also you can ask Allah to protect you from this happening again.

I hope that your financial situation improves and you will be feeling better soon!