She has received a marriage proposal from a person who has some shortcomings which she is trying to deal with and discuss
The basic principle is that if a woman receives a marriage proposal from a man whose religious commitment, attitude and trustworthiness are satisfactory, then she should accept, so long as there is not another offer from one whose attitude and religious commitment are better. So if the one who has proposed marriage to you meets these criteria, and he is keen to learn more about Islam as you say, then this is a good sign. But if the shortcomings to which you refer in your question are major sins or sins in which he is persisting or committing openly, then we advise you to wait for someone better, so long as there is no risk of you doing something haraam or exposing yourself to greater fitnah (temptation).
It is not necessary in the case of istikhaarah to feel something specific afterwards. Rather if you consult people and think deeply about the matter, and it becomes clear to you that this matter will be beneficial both in religious and worldly terms, then you should pray istikhaarah and go ahead, and not wait for a sign or a dream or a feeling. You should rather put your trust in Allaah and go ahead after praying istikhaarah. You will find a detailed answer concerning istikhaarah and its rulings in Question no. 5882.
Beware of being alone or of uncovering in front of this man who is still a non-mahram to you. In the answer to question no. 12182 you will find a detailed answer to your question regarding marriage proposals and sitting with and meeting the one who has proposed marriage to you. Please refer to this question.
Your wish concerning what you hope to find in a husband, meaning that he lives for the sake of Allaah, is a great wish, and we hope that Allaah will grant you that. But you should know that a righteous woman is one of the greatest means that will help a man in this regard, by helping him and advising him, and encouraging him to do more, and patiently putting up with anything that affects her rights because of his being involved in doing righteous deeds.
We ask Allaah to help you to do that which is good. Ameen.
Sheikh Muhammed Salih Al-Munajjid