The Bible repeatedly tells us that God will have mercy on whom He has mercy

Lutero said:

Romans 9:

14 What shall we say then? There is no injustice with God, is there? May it never be! 15 For He says to Moses, “I WILL HAVE MERCY ON WHOM I HAVE MERCY, AND I WILL HAVE COMPASSION ON WHOM I HAVE COMPASSION.” 16 So then it does not depend on the man who wills or the man who runs, but on God who has mercy. 17 For the Scripture says to Pharaoh, “FOR THIS VERY PURPOSE I RAISED YOU UP, TO DEMONSTRATE MY POWER IN YOU, AND THAT MY NAME MIGHT BE PROCLAIMED THROUGHOUT THE WHOLE EARTH.” 18 So then He has mercy on whom He desires, and He hardens whom He desires. 

The Bible repeatedly tells us that God will have mercy on whom He has mercy.

That doesn't mean that God is capricious. God has revealed upon Whom He bestows His mercy:
Exodus 20:6

King James Version (KJV)
⁶ And shewing mercy unto thousands of them that love me, and keep my commandments.

God also points out that His mercy does not depend on man - his willing or his running - BUT ON GOD WHO HAS MERCY.

That is true. But God's criteria for man is that man must obey God in order for God to show His mercy upon man:
Matthew 25:31-45

King James Version (KJV)
³¹ When the Son of man shall come in his glory, and all the holy angels with him, then shall he sit upon the throne of his glory:
³² And before him shall be gathered all nations: and he shall separate them one from another, as a shepherd divideth his sheep from the goats:
³³ And he shall set the sheep on his right hand, but the goats on the left.
³⁴ Then shall the King say unto them on his right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world:
³⁵ For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in:
³⁶ Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me.
³⁷ Then shall the righteous answer him, saying, Lord, when saw we thee an hungred, and fed thee? or thirsty, and gave thee drink?
³⁸ When saw we thee a stranger, and took thee in? or naked, and clothed thee?
³⁹ Or when saw we thee sick, or in prison, and came unto thee?
⁴⁰ And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me.
⁴¹ Then shall he say also unto them on the left hand, Depart from me, ye cursed, into everlasting fire, prepared for the devil and his angels:
⁴² For I was an hungred, and ye gave me no meat: I was thirsty, and ye gave me no drink:
⁴³ I was a stranger, and ye took me not in: naked, and ye clothed me not: sick, and in prison, and ye visited me not.
⁴⁴ Then shall they also answer him, saying, Lord, when saw we thee an hungred, or athirst, or a stranger, or naked, or sick, or in prison, and did not minister unto thee?
⁴⁵ Then shall he answer them, saying, Verily I say unto you, Inasmuch as ye did it not to one of the least of these, ye did it not to me.

But, if you want to live under the Law, then you are welcome to do so. Those who choose to live under the Law will be judged by that Law.

That is true. And the Law leads one to Christ:
Galatians 3:24

King James Version (KJV)
²⁴ Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.

It is those who keep the Law, whom God justifies:
Romans 2:13

King James Version (KJV)
¹³ (For not the hearers of the law are just before God, but the doers of the law shall be justified.

I will choose to live under the mercy of God.

If you want to live under the mercy of God, you must obey His Commandments:
Deuteronomy 7:9

King James Version (KJV)
⁹ Know therefore that the Lord thy God, he is God, the faithful God, which keepeth covenant and mercy with them that love him and keep his commandments to a thousand generations;

Matt 5:7 expresses it another way "Blessed are the merciful, for they will be shown mercy."

Again, revisit Matt 25:31-45 and you will see that verse explained.

The reverse of that is Scripturally true - Judged are the Law-keepers, for they will be shown the Law.

You have misspoken. Juded are the Law keepers, for they shall be saved. Those who keep the law have already seen the law. But the lawless are condemned:
Romans 8

King James Version (KJV)
⁴ That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit.
⁵ For they that are after the flesh do mind the things of the flesh; but they that are after the Spirit the things of the Spirit.
⁶ For to be carnally minded is death; but to be spiritually minded is life and peace.
⁷ Because the carnal mind is enmity against God: for it is not subject to the law of God, neither indeed can be.
⁸ So then they that are in the flesh cannot please God.

1 Pet 2: 9 But you are a chosen race, a royal priesthood, a holy nation, a people for his own possession, that you may proclaim the excellencies of him who called you out of darkness into his marvelous light. 10 Once you were not a people, but now you are God’s people; once you had not received mercy, but now you have received mercy.

Yeah, because we have received the Sacraments, wherein God sheds His Mercy upon our soul:
Titus 3:5

King James Version (KJV)
⁵ Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;

Sincerely,

De Maria