Why does the Mosaic Law demand the death of so many innocent people?

Your real question is really why do the sins in these three instances deserve Death in God's eyes?

Leviticus 20:13,  Exodus 35:2, Deuteronomy 21:18-21.

The answer to that is the same as why God demanded death for when Adam and Eve disobeyed God, and ate from the tree of the knowledge of good and evil.

Genesis 2:17 KJV

But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

God had created man in his image, and he had created both man and woman. In that original creation God did not give them or any of their prosperity the knowledge of good and evil.

Genesis 2:7 KJV

And the LORD God formed man of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.

Eve was created to be Adam's helper:

Genesis 2:18, 21, & 22 KJV

18 And the LORD God said, It is not good that the man should be alone; I will make him an help meet for him.

21 And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof;

22 And the rib, which the LORD God had taken from man, made he a woman, and brought her unto the man.

God created them differently for a reason, and that reason was:

Genesis 1:26 through 28 KJV

26 And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepeth upon the earth.

27 So God created man in his own image, in the image of God created he him; male and female created he them.

28 And God blessed them, and God said unto them, Be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.

Man was not created as an after thought God had specific plans for man. When God created Adam, before he created Eve he gave Adam an assignment.

Genesis 2:5 & 15 KJV

5 And every plant of the field before it was in the earth, and every herb of the field before it grew: for the LORD God had not caused it to rain upon the earth, and there was not a man to till the ground.

15 And the LORD God took the man, and put him into the garden of Eden to dress it and to keep it.

God had also created Adam as an eternal being.

Genesis 2:16 & 17 KJV

16 And the LORD God commanded the man, saying, Of every tree of the garden thou mayest freely eat:

17 But of the tree of the knowledge of good and evil, thou shalt not eat of it: for in the day that thou eatest thereof thou shalt surely die.

So when Man disobeyed God and ate from the tree of the knowledge of good and evil, lost that eternal life, and also marred what God had already pronounced as good.

Genesis 1:31 KJV

And God saw every thing that he had made, and, behold, it was very good. And the evening and the morning were the sixth day.

So now that man had given up his eternal life, when Adam died there would be left no one to tend the earth and till the soil.

Therefore in order for those duties to be carried on man had to procreate, and so God told man to be fruitful and multiply and fill the Earth. So man even though he had given up life eternal on the Earth, God still needed to fulfill his overall plan.

As for the part about h*m*sexuality, For that you have to consider that God meant for man to procreate for several reasons, and one purpose was to have Adams posterity to care for his creation, that is why he gave sex to mankind in the beginning, and his explicit instructions were to multiply and fill the Earth. Sex was given to mankind for that reason, not for his pleasure. God made it pleasant so that man would not think of it as strictly a duty to him, even though it was. And there is no procreation in h*m*sexuality, and it is therefore an abomination to God in that it is relegated to a place of pleasure only and not to fulfill God's edict to fill the Earth.

Leviticus 20:13 KJV

If a man also lie with mankind, as he lieth with a woman, both of them have committed an abomination: they shall surely be put to death; their blood shall be upon them.

But you have singled out only one of many sexual deviations for which God has pronounced physical death and all of those are for the same reason and that is the misuse of sex.

As for the punishment of physical death for breaking the Sabbath God gave man a specific command;

Exodus 20:10 & 11 KJV

10 But the seventh day is the sabbath of the LORD thy God: in it thou shalt not do any work, thou, nor thy son, nor thy daughter, thy manservant, nor thy maidservant, nor thy cattle, nor thy stranger that is within thy gates:

11 For in six days the LORD made heaven and earth, the sea, and all that in them is, and rested the seventh day: wherefore the LORD blessed the sabbath day, and hallowed it.

God blessed the Sabbath and made it holy and is to be observed as a covenant to the LORD.

Exodus 31:15 & 16 KJV

15 Six days may work be done; but in the seventh is the sabbath of rest, holy to the LORD: whosoever doeth any work in the sabbath day, he shall surely be put to death.

16 Wherefore the children of Israel shall keep the sabbath, to observe the sabbath throughout their generations, for a perpetual covenant.

We do not have the right to degrade the Sabbath and ignore it's significance.

As for the last part of your question, concerning disobedient children.

Again God gave a specific command in the 10 commandments, and with this command, and none of the others, God gave the reward for obedience.

Exo 20:12 KJV

Honour thy father and thy mother: that thy days may be long upon the land which the LORD thy God giveth thee.

Deuteronomy 21:18 through 21 KJV

18 If a man have a stubborn and rebellious son, which will not obey the voice of his father, or the voice of his mother, and that, when they have chastened him, will not hearken unto them:

19 Then shall his father and his mother lay hold on him, and bring him out unto the elders of his city, and unto the gate of his place;

20 And they shall say unto the elders of his city, This our son is stubborn and rebellious, he will not obey our voice; he is a glutton, and a drunkard.

21 And all the men of his city shall stone him with stones, that he die: so shalt thou put evil away from among you; and all Israel shall hear, and fear.

So it only stands to reason that if you do not honor your parents you should expect that your days will not be long, and matter of fact the less you honor them the shorter you should expect them to be right up to the point of not having any more days.