Tips from dev (mostly spoiler free)

Game basics and some tools

Game Basics

1.
Each circle under the board represents a rule.
All boards in the same level shares the same rule set, while different level have different rules.
For example, 1-1's first rule is start at circle, second rule is end at square.
1-2's first rule is start at square, second rule is end at circle.

2.
The first board of each level starts with a dotted line as a clue.
Sometimes the dotted line can be misleading.
Sometimes the dotted line isn't misleading, but you are misleading yourself.
I'd recommend do a few more tests on board 1 before moving to the next one.

The last board of each level hides its rules to prevent (or at least increase the cost of) solving a level without understanding its rules.

3.
Write down your thoughts should help.

4.
Each symbol on the level selection screen represents something.

5.
The rules are independent to each other.
( 1-6-5 is a good example.)
Work out the rules one by one instead of trying to satfisy all of them at once.

6.
Each rule can be described with one sentence.
If you can't describe your assumption with one sentence, you might be overthinking.

7.
All ? levels are about "think outside the box".
Hope you can enjoy.

Tools

1.
The most powerful method in this game is trial and error.
For example, if you guess the first rule is "visit all squares", you can forget about other rules, just draw multiple lines on different boards to test:
When all squares are visited, is the first rule correct?
When at least one square is not visited, is the first rule wrong?
If you had a good outcome, move on to the next rule.
Otherwise, make a new guess. (Don't forget what breaks your previous guess, new attempt should cover that case)

2.
A common tool in draw-one-line puzzle games is called Coloring.
To do so, color the board as a chess board.
Here is a 5*5 example:
XOXOX
OXOXO
XOXOX
OXOXO
XOXOX
As you can only move orthogonally in the game, all X must be followed by O, and all O must be followed by X.
In another word, even numbered box in your line must be of one color, and odd numbered box must be of the other color.

Conclusion:
When you are drawing a line of even length, the start and end position must be in a different color. Of odd length, they must be in same color.
In an odd * odd board, the color in corner has one more box than the other. So if you want to visit all boxes, you must start and end in that color.
It's impossible to visit two more boxes of one color than another.

3.
Another common tool in draw-one-line puzzle games is called Microsoft Paint.
When you've understand the rules and still can't solve a big board, just take a screenshot and paste it to ms paint.
You may want to draw different parts of the line and try to connect them, or visualize the effect of some symbols.
For example, if a rule is "each circle is a knight, you can't pass any box within a knight's move", mark all these boxes to avoid them.
(Clarification: This is just an example, there is no chess related rule in the game.)

It becomes even more powerful in the late game, when everything gets weird.

[Viridian]

I solved 2-7 through guessing. The only rule I am certain of is
The line must be 4 squares long would you mind telling the other rules? Lot's of guides online but they just show the answers.

[dholland]

Not sure you can actually work out all the rules separately for all puzzles. Frequently you get 2 rules satisfied together. For example, with puzzle 7.3 I found ways to get rule 1 and 2 on all puzzles without solving them all, and ways to get rule 3 only on all the puzzles, without knowing the rule (an empty verification), but couldn't isolate any of the rules. I guessed rule 1 and my tests were verified. I guessed a combination for rules 1 and 2 together and my tests were verified. I hadn't solved everything, so I knew there was something else and eventually guessed it by trying some different things on one of the puzzles until I solved it. Still have no idea what the rules were apart from rule 1, but I had a few sentences describing everything needed to solve all the puzzles. Hope that helps.