Is our success predestined by our past karma?

In some sense yes. Everything is happening for a reason. So do your choices in another incarnation reflect your choices in this incarnation? Yes, because each time it is you that is doing the choosing.

So in a sense you could say. Yes you are affecting yourself.

These ideas are found in the Cula-kammavibhanga Sutta, however this sutta is questionable both in terms of its composition (see this discussion) & its actual reality.

We can see in the actual reality of the world some of the most wealthy people do very evil things to acquire their wealth & some of the most beautiful people live emotionally afflicted lives. It is highly improbable that such people did something exceptionally good in a past life & then became so evil & neurotic in the next life. Further, we can know exactly the steps a person look in this life to become wealthy, as written in their biographies (eg. Bill Gates). This shows their wealth is unrelated to any actions performed in a past life.

No, it is determined by many other qualities in a person.

Courage, awareness etc.

Kamma is volitional or intentional action as Buddha said, “It is volition, bikkhus, that I call kamma. For having willed, one acts by body, speech, or mind.” It’s results ripens or takes effect in three ways; to be experienced in this very life, the next rebirth or at some subsequent occasion. Thus, as long as we travel on in the cycle of rebirths, our stockpile of kamma will yield its due results. We have no escape from kamma so long as we make no effort to make an end to kamma by becoming at least a Stream Winner. Until one gets into the path, as Buddha said, “beings are the owners of their kamma, the heirs of their kamma; they have kamma as their origin, kamma as their relative, kamma as their resort; whatever kamma they do, good or bad, they are its heirs.”

In this way, the effect of ones past kamma determine the nature of ones present situation in life. This is a universal principle, on which Buddhist morality is based. It does not assert that everything is due to Kamma. If everything were due to Kamma, a man must ever be bad, for it is his Kamma to be bad. One need not consult a physician to be cured of a disease, for if one's Kamma is such one will be cured.

Kamma is only one of the five all-embracing five orders or processes which are laws in themselves. The other four ‘Niyamas’ which operate in the physical and mental realms other than the Kamma Niyama are… Utu Niyama, Bija Niyama, Citta Niyama, & Dhamma Niyama. Utu Niyama is that of the physical order such as seasonal phenomena of winds and rains. Bija Niyama is the order of germs or seeds. Citta Niyama is the order/power of the mind. Dhamma Niyama is that of those who tread the Path. Kamma is, therefore, only one of the five.

It is this doctrine of Kamma that can explain all the inequality of mankind. But it does not mean fate as it is possible to change or reduce the effects of these past actions through present actions. That is why if a person who has much money, but no true, righteous friends should practice sila. Such people who have no friends, very often single but keep on hoarding wealth have in their past lives given lavishly in generosity as dana but without any sila/morals in them. A person who is very generous but not virtuous (without the any personal virtue like the observance of the five precepts ) would inherit this kind of bad kamma. Even today many rich people are highly generous but the inevitable karmic law is that no degree of generosity can cover up the lack of virtue in personal life. This karmic law cannot be deceived. This is why it has been laid down that "give dana with confidence and always be virtuous" (daanam dadantu saddhaaya - seelam rakkhantu sabbadaa). The two aspects should be complementary to each other.