4 puzzles

First one is: 96481.
Sq numbers with increasing digits in each term.

Others might take time for me

4 is 553141784, 998131743

Ratings should be at least ~30 points lower.

Last one left, 3, is: 876543, 3456789, 98765443, 344567899, 9987654431
Always adding front or back and flipping doesn’t work so I assume they just go in order.

Two remaining:

2. 1378 (1 from 1st, 3 from 2nd...8 from 5th)
3. 8765, 5678, 8765432

maybe #2 is "1378"
my logic is that every time one number is removed, and its alternating between 4th and 8th number from the left that is removed

One possible pattern/solution for problem 2 (although a bit childish) may be:

123456789 number 2, 2nd position (+4, +3)
1 3456789 number 6, 5th position (+3, +2)
1 345 789 number 9, 7th position (-5, -4)
1 345 78 number 4, 3rd position (??, ??)
1 3 5 78 ?? ??
??

Starting from (4,3), I tried smaller paired changes:

(+3,+2) -> number 7, 5th NO (it's not fifth)
(-3,-2) -> number 1, 1st YES

(+2,+1) -> number 6, 4th NO
(-2,-1) -> number 2, 2nd NO

(+1,0) -> number 5, 3rd YES, but ultimately NO since both values must change (that's how I thought of it)
(-1,0) -> number 3, 3rd NO

So, maybe it's 3578...but again, the "pattern" I think I see is a bit childish.