We have a study on our web site called, Financial Faithfulness which will answer some of your questions especially in regard to the tithe. I would also suggest that you carefully read 1 Cor. 16:1-3 and 2 Cor. 8-9 for some basic principles of giving and managing money in the church. As you read these passages, note the strong emphasis against any type of coercion and manipulation and how Paul was extremely careful that all money be handled in a way that would protect both the church and those involved with its collection and distribution from any appearance of mishandling of the funds.
Many, if not most churches pass an offering plate, but in view of the focus in 2 Cor. 8-9 on giving of one’s own accord, not grudgingly or out of a sense of compulsion, but voluntarily from a readiness of heart and mind, I do not believe this is the most biblical method for receiving the gifts of the saints. While pastoring churches for some 28 years, I always taught and worked toward some method of giving that avoided this. It usually took some time, but in most cases we did away with passing an offering plate. No matter how you look at it, passing a plate down every row brings with it a certain amount of pressure and is somewhat coercive. A simple way to avoid this is to have a collection box or more placed conveniently where the body of believers may simply drop their gifts or offerings of their own accord as they enter or go out. To further the non-coercive element, during the first part of the worship and Bible study time, I would generally make a comment such as, “Giving is a privilege for believers in Christ. It is to be done not grudgingly or out of a sense of compulsion (cf. 2 Cor. 9:7), but out of sense of stewardship having first given oneself to the Lord and out of faith in God’s grace (see 2 Cor. 8:1f). If you are here today without Christ as your personal Savior, we do not ask that you give, but rather that you would consider receiving Christ by faith as God’s gift to you.”
Concerning the managing of the funds, this is part of the responsibility of the church leadership that God has raised up to lead the church. But it must, as mentioned above, be done above board and in such a way that there can be a careful accounting of how much comes in and exactly where every penny is spent. This is needed to protect those involved from temptation and false accusations and to protect the church from problems. For instance, it is wise to always have more than one person count and record the money collected. This is not because we might not trust the person, but to protect them and to demonstrate a commitment to honest and above board behavior.
In view of Malachi 3:10, some teach that all giving should be brought to the local church and from there should be dispersed to the various ministries and missions of the church. This was a part of the OT system under the Law, however, and should not be forced on the church today. No such directions or commands are given in the NT. While believers are responsible to give to their local ministry to meet its needs, believers should be free, under the leading of the Spirit, to give to other needs as they see them and are able to help. But for even this there are some principles that guide us. Compare Galatians 6:6-10; 3 John 5-8; Ephesians 4:28; 1 Thessalonians 4:11.