(1)
Where there's a will, there's a way.
Meaning: If someone has the desire and determination to do something, he or she can find a method for accomplishing it.
My interpretation: I partially agree on the translation mentioned above, in the sense that you will succeed only if you have the desire. However, desire seems to be a required but insufficient condition; we may still fail even if we desire to succeed. I think the most important take-away message here is the great power of positive pshychological hints. If we believe that we can achieve something good (e.g., unlock our full potential), we should hold that belief firmly and remind ourselves frequently. By working hard towards the goal, we will definitely harvest some success, even if we cannot realize the initial goal.
(2) 
Meaning: Let nature take its course, or let it be.
My interpretation: With an initial look at this proverb, we may find it to conflict with (1), as it seems to encourage us to do nothing and passively wait for things to happen naturally. Certainly, nothing good can happen if we lie down and do nothing. However, with some deep thinking, I feel that this proverb complements (1), and the two proverbs instruct us to balance between work and life, and to happily accept both success and failure. To me, this sentence means that when we work hard towards a goal, do not worry too much about the outcome or result. Instead, focus on the process and pay close attention to our every step in the procedure. Do not worry that bad things may happen; do no imagine that good things do not show up finally. Just do whatever we can towards the goal, believe in good outcomes, and then trust the nature to take its course. When combining (1) and (2), we can basically learn of the following concept: No matter whether our goal is to publish a paper, obtain a PhD degree, recover from a serious disease, or overcome our weakness, let's (i) set the pace for our progress, not too fast as that can make us tired and bored easily, not too slow as that can distract us from our target, and (ii) move forward steadily. While we enjoy the process of pursuing our dream, our subconsciousness and the nature will do us a favor and work out the remaining things for us.
(3)
Online translation: Where there is a will there is a way. Breaking cooking pots, sinking their ships. The one hundred and two Qin cities were over-run by Chu finally. Man of firm resolve ne'er forsaken by Fate. But one needs to endure great hardship. Just three thousand armoured Yue troops obtained the great victory over Wu did scoop.
My interpretation: This is a couplet--an extended version of the proverb (1). The extension includes another sentence to emphasize the same idea, together with two historic events to support the argument. The additional sentence means "God helps those who help themselves". The two events are separtely related to two celebrities in Chinese history: XIANG Yu (223-202 B.C.), the King of Western Chu during the Chu-Han Contention period of China, and Goujian (496-465 B.C.), the king of the Kingdom of Yue.
In 207 B.C., Xiang's army (also named as "Chu forces") crossed a river to attack the Qin forces. It seemed impossible for Xiang's army to defeat their enemies, as they had a lot fewer soldiers and lacked food supplies. To enhance the troop morale, Xiang ordered his men to sink their boats and keep only three-days rations after crossing the river. In this way, his men only had two choices: to either beat the enemies for survival or get beaten by the enemies to death. Consequently, Xiang's soldiers became very courageous, because they knew that fear does not help them survive, neither does surrender; instead, the courage does. Despite being heavily outnumbered, Chu forces finally scored a great victory after nine engagements, defeating the 300,000 Qin soldiers with 20,000 soldiers. This battle significantly shook the foundation of Qin dynasty, contributed to the death of that dynasty, and indicated a brand new dynasty created by Xiang. There are only a few cases in Chinese history where the few defeat the many, and this battle of Xiang is one among those few cases. Even today, I still consider the event to be a miracle, but the miracle did happen because of the strong will of Xiang and his men.
In the warring state period in Chinese history (722-481 B.C.), there were several small countries located in different parts of the current China's territory. These countries frequently fought with each other; each country tried to overrun and control all other countries. Among these countries, the Kingdom of Yue and the Kingdom of Wu also fought a lot. In 494 B.C., Goujian's army (of the Kingdom of Yue) was defeated by the army of the Kingdom of Wu. Goujian was captured, and forced to work for years as a servant for Fuchai--the king of the Kingdom of Yue. Obviously, it had been a huge disgrace and shame for a king like Goujian to be captured and forced to serve other people. However, to eliminate Fuchai's doubt in him and to avoid Fuchai's further persecution, Goujian hid his disgrace, pretended to be satisfied with being a servant, worked diligently to demonstrate his loyalty to Fuchai, and expressed no interest in politics or his home country. Goujian's excellent performance in front of Fuchai finally eliminated Fuchai's doubt, and earned Goujian a great opportunity of going back to the Kingdom of Yue. Ever since then, Goujian intentionally slept on firewood in nights and tasted the bitterness of animals' gall bladder at home. By creating the uncomfortable sleeping condition and sense of taste, Goujian tried to remind himself that he should never ever forget the huge disgrace and shame he had felt and experienced in the Kingdom of Wu; he told himself to patiently prepare for a future battle with Fuchai's army and to destroy his enemies in that battle. After working hard together with his people for years, Goujian finally defeated Fuchai and wiped out the Kingdom of Wu.