Regarding the 17th Amendment, now instead of state legislatures appointing senators as restraints on the Federal government, the people now do so directly by electing senators themselves. State legislators can and do gerrymander their own districts. Electing senators bypasses that.
The part of the law that would prohibit a president from pardoning himself, his own family or members of his own administration. Hypothetically, it would take a subsequent president to pardon Trump family members unless they were also members of the Trump/Pence Administration; not Pence 46; he's also part of that administration.
It looks like a strategic error on Rep. Cohen's part to tie the two parts of the bill together. Senators from small states would never vote to reduce the clout of their own states. They may well favor restrictions of presidents' pardoning power but instead of legislation would it take a constitutional amendment to do so? I don't know.