Answer to Question 1:
I do not believe knowing the author is important.
It may not be important to you, but it is rather important to me and that's why I asked the question.Therefore, I will ask again who the author is.

The better question to ask might be: “Where in the word of God is this saying supported?” The answer to that question is the very next verse in Matthew.
Matt 7:24-25 says: Every one therefore that heareth these words of mine, “and” doeth them, shall be likened unto a wise man, who built his house upon the rock: and the rain descended, and the floods came, and the winds blew, and beat upon that house; and if fell not: for it was founded upon the rock. ASV
The “and” is not there by accident. Would it not be biblical to understand that the purpose of “and” is to let the reader know that Jesus has two expectations here, not just one? The first is to “know” his will by going to his word to hear what he has to say. After knowing his will, the wise man is to “do” his will. Knowing clearly come before doing here.
Although it is certainly true that the 'doers of the Word and not the hearers of the Word' shall be saved (Matt 12:50; Lk 11:28; Rom 2:13; Jam 1:22-25; 1Jh 2:3). The point Jesus' parable here of the two builders is something far more important. The parable contrasts two builders which is typical of the teachings of Christ, i.e., dividing the world into two groups and two groups only (cf. 6:22,23; 7:13,14; 7:17,18; 10:39; 13:11,12,14-16,19-23; 24:30,36-42,47-50; 22:1014; 25:2). Both of these men build houses, which for all intents and purposes look much the same. They use the same materials, put as much effort into constructing them, etc. But the main and critical difference is the
foundation upon which they build these houses. The wise (sensible) man built his house upon rock. The foolish man built his house upon sand or gravely ground. The wise man listens to the words of his Lord and then out of a heart of gratitude in response to the salvation given him, puts them into practice. The foolish man, in sheer contrast, heeds not to the words of God but rather listens only to his own voice out of self interest and thinks little of the future. Consequently, when the tests of life come, the foolish man's house is destroyed. However, these earthly tests are but shadows of the great 'test' which is to come; the Final Judgment wherein the wise man is received by God because he is grounded upon the Rock, i.e., Christ and the wise man is rejected because he is without Christ.
Thus, the parable's main thrust isn't upon
doing the Word but rather upon
being united with the Word, i.e., the Logos; the Lord Christ. The doing of the Word is not an injunction to do but an indicative of what is. The wise are those who have been embraced by Christ and THEREFORE conduct their lives in loving submission to His will.
Also consider Eph 6:5-6 which says: “Servants, be obedient unto them that according to the flesh are your masters, with fear and trembling, in singleness of your heart, as unto Christ; not in the way of eyeservice, as men-pleasers; but as servants of Christ, doing the will of God from the heart;” ASV
In this case, would it not be biblical to conclude the heart is the place where we “know” God’s will and would not knowing God’s will come before “doing” God’s will here?
Sorry, but I don't see that as what this passage is saying, i.e., "[i]the heart is the place where we 'know' God's will...". Paul is setting for the
motive behind one's obedience; superficially vs. lovingly (cp. Deut 6:5; 30:20; Matt 22:37; Mk 12:30 and Col 3:22).
I agree with the principle truth that one must know the will of God before one can do the will of God. (cf. Col 1:9,10)
Answer to Question 2:
The meaning of “we need to do God's will before we can become it” can also be seen above in the words of Eph 6:6. Some explanation may be needed to see it.
Consider the wording in 2 Cor 9:7 (Let) each man (do) according as he hath purposed in his heart: not grudgingly, or of necessity: for God loveth a cheerful giver. ASV
Here it is clear that a person can do God’s will with a wrong attitude/heart. This is “doing” without “being”.
Becoming God’s will can also be seen in Rom 12:2 which says:
And be not fashioned according to this world: but be ye transformed by the renewing of your mind, that ye may prove what is the good and acceptable and perfect will of God. ASV
Notice here that “transformation” comes as a result of doing God’s will (i.e. renewing the mind can happen when we use time to hear, read, memorize or meditate on God’s word). Also notice that the “purpose” of transformation is to “prove what God’s will is”. Is this not becoming God’s will?
Sorry, but I simply do not find the phrase "become God's will" anywhere in Scripture. This is one of the reasons for my asking who the author was, i.e., whether this is an idea that you have created or whether this is something someone else has been preaching/teaching or written in a book.
What I do read in Scripture is that true believers become "holy" (Eph 1:4; 2:10; 1Thess 4:7; Heb 12:10), "conformed to the image of Christ" (Rom 8:29; 13:14; 2Cor 3:18; Col 3:10) and "partakers of the divine nature of Christ" (2Pet 1:4; Jh 1:12; Eph 4:23-24; 1Jh 3:2). In short, we are not becoming God's will but like Christ who is the effulgence of His, God's glory (Jh 1:14; Heb 1:3).
Lastly, go back to the house that stands in Matt 7 above. There, the result of knowing and doing is standing. Has not that “standing house” become the will of God?

The wise man who built the house upon rock (Christ) is not subject to destruction, either those typological tests in this life but especially the just judgment of God on that last day. It is the
foundation that upholds the house and not the materials or design of the house in and of themselves. The passage says nothing of the house (builder) becoming anything, especially "the will of God".