What two things does Jane learn at Moor House (other than her inheritance)?

The chapters you want to focus on are 33 and 35 to answer this question. Chapter 33 details how St. John one snowy night comes to Jane´s school house and tells her about her uncle dying and then the inheritance she has received. He also tells her how she and St. John and his sisters are related - they are cousins. This chapter is also when Jane realises that St. John knows who she really is and her past relations with Rochester. Take note of how important the realisation that Jane has family is to her. After many chapters of thinking she was in the world by herself, finally she has family that she can call her own, and this is of far more worth than money:

Glorious discovery to a lonely wretch! This was wealth indeed! - wealth to the heart! - a mine of pure, genial affection. This was a blessing, bright, vivid, and exhilarating - not like the ponderous gift of gold: rich and welcome enough in its way, but sobering from its weight.

To Jane, this discovery is of far more importance than her inheritance, and marks her rise, not just in terms of wealth, but also in terms of connections - a vital aspect of life in Victorian society. Note how it is described as though it were gold, but not "sobering in its weight".

Chapter 34 and 35 marks the discovery that her cousin St. John wants to marry her - but not for love, only so he can have a suitable work-mate to help him with his missionary work. Jane finally finds the strength to refuse him and at the end of the Chapter she "hears" Rochester´s voice calling to her, which is very important as it gives her the strength to break free from the constricting relationship with St. John and leave to find Rochester. Note how Jane ends this chapter:

I broke from St. John; who had followed, and would have detained me. It was my time to assume ascendancy. My powers were in play, and in force.

This is the knowledge or the "push" that Jane needs to assert herself and her own will to live her own life rather than being pushed into living the life others would have her live.