Is it necessary to exercise faith to obtain answers to our prayers?
Yes
Mark 11:24 (KJV) 24 "Therefore I say unto you, What things soever ye desire, when ye pray, believe that ye receive them, and ye shall have them."
Matthew 21:22 (KJV) 22 "And all things, whatsoever ye shall ask in prayer, believing, ye shall receive."
James 1:5-6 (KJV) 5 "If any of you lack wisdom, let him ask of God, that giveth to all men liberally, and upbraideth not; and it shall be given him. 6 But let him ask in faith, nothing wavering. For he that wavereth is like a wave of the sea driven with the wind and tossed."
"Every saint who comes to God with a true heart, and sends his honest petitions to Him in faith, will have his prayers answered. Your faith must not let go of the promises of God, if you do not see or feel the immediate answer to your prayers. Be not afraid to trust God. Rely upon His sure promise: “Ask, and ye shall receive.” John 16:24. { CCh 345.1}
God is too wise to err, and too good to withhold any good thing from His saints that walk uprightly. Man is erring, and although his petitions are sent up from an honest heart, he does not always ask for the things that are good for himself, or that will glorify God. When this is so, our wise and good Father hears our prayers, and will answer, sometimes immediately; but He gives us the things that are for our best good and His own glory. God gives us blessings; if we could look into His plan, we would clearly see that He knows what is best for us and that our prayers are answered. Nothing hurtful is given, but the blessing we need, in the place of something we asked for that would not be good for us, but to our hurt. { CCh 345.2}
I saw that if we do not feel immediate answers to our prayers, we should hold fast our faith, not allowing distrust to come in, for that will separate us from God. If our faith wavers, we shall receive nothing from Him. Our confidence in God should be strong; and when we need it most, the blessing will fall upon us like a shower of rain." 615 { CCh 345.3} —Mrs. E. G. White, Counsels To The Church, 345.3
"To have faith in the promises of God, to walk forward by faith, pressing on without being governed by circumstances, is a lesson hard to learn. Yet it is a positive necessity that every child of God learn this lesson. The grace of God through Christ is to be ever cherished; for it is given to us as the only way of approaching God. Faith in the words of God, spoken by Christ enshrouded in the pillar of cloud, would have enabled the children of Israel to leave a record of a very different character. Their lack of faith in God gave them a very checkered history." MCP 535-535
"If we would give more expression to our faith, rejoice more in the blessings that we know we have--the great mercy, forbearance, and love of God--we would daily have greater strength. Have not the precious words spoken by Christ, the Prince of God, an assurance and power that should have great influence upon us, that our heavenly Father is more willing to give the Holy Spirit to them that ask Him than parents are to give good gifts to their children?"--Lt 7, 1892. (2SM 243.)
"Let us put away everything like distrust and want of faith in Jesus. Let us commence a life of simple, childlike trust, not relying upon feeling but upon faith. Do not dishonour Jesus by doubting His precious promises. He wants us to believe in Him with unwavering faith."--Lt 49, 1888.
"Keep looking unto Jesus, offering up silent prayers in faith, taking hold of His strength, whether you have any manifest feeling or not. Go right forward as if every prayer offered was lodged in the throne of God and responded to by the One whose promises never fail. Go right along, singing and making melody to God in your hearts, even when depressed by a sense of weight and sadness. I tell you as one who knows, light will come, joy will be ours, and the mists and clouds will be rolled back. And we pass from the oppressive power of the shadow and darkness into the clear sunshine of His presence.--Lt 7, 1892." (2SM 242, 243.)
"We must "talk faith, … live faith, … act faith, that [we] may have an increase of faith. Exercising that living faith, [we] will grow to strong men and women in Christ Jesus.” {FW 78.2}
"My soul is tired of hearing tame prayers—prayers offered by those who do not believe that they will receive what they ask for. These prayers hurt my soul, because I remember that Christ died in order that a whole heaven of opportunities and privileges might be brought within the reach of fallen humanity. Yet many act like helpless babes. {Ms85-1901.23} ... If you send up your petition to God, He says He hears you. What is your evidence? Do you feel any better than before? Do you think of and examine your feelings to see if some great change has taken place within? You should step out on the Word of God, and go straight forward, knowing that He answers your prayers, because He has promised to give, if you ask. Thus by exercising faith, bring about the answer to your petitions. As you work to answer your own prayers, you will find that God will reveal Himself unto you as He does not unto the world." {Ms85-1901.33}
There are many more statements on the need to have faith when we pray. One thing that helps me have faith, is to end my prayers by thanking the Lord that He has heard me and is answering. Doing such a thing may help you too.—Dan