When life gives you lemons run away or face the ciphers of entrapment

Question

Clearly that lemon you got last night from that peculiar street peddler was drugged, because you find yourself not at home like you're supposed to be at first light.

As you get up and start looking around you see a piece of paper stuck to a door (which is of course unfortunately locked). This is what the paper reads:

Hello!
Welcome to my wonderful cage.

Of course you probably don’t feel the same as I but it doesn’t matter as the only way for you to leave is to solve these wonderful little puzzles I made just for you. There are four in all.
Some are harder than other of course but I’m sure you’ll make due. I highly recommend you take this paper with you as it’s the only one and once you pass through this door it locks.

Anyhow, here are your keys for the four doors:

The first door requires a 5-letter word, I wonder if you can read these patterns… probably not:

The second door requires a 4-letter word, however you only get to have these symbols and equations instead:

The third door requires a 7-letter word, let’s see if you’ll understand this one:

 mpmpfffmfmfmmfmmppmpm

The fourth and final door requires a 6-letter word, many people can find these confusing, and so you’re not alone:

Once you unlock the fourth and final door, you’ll be free to go. I will never intentionally capture you again, although I can’t speak for my colleagues, they may want you too.

So, having no other real choice you take the paper and begin trying to escape. After passing through the final door you get outside and are quite happy with yourself. Until you realize that there’s an unscalable locked gate in front of you with another paper attached to it:

I hope you remember how you opened the doors as it’s the only way to get out of here. hahaha!

What is the phrase to escape to locked gate?

Answer 1

The first is

international maritime flag code for NEVER.

The second is

Babylonian numerals: taking the final solution to each equation and converting (A=1, B=2...) gives HOLD.

The third is

Kenny Code for DRUGGED.

The fourth is

Mayan numerals for 7/4, 1/5, 8/9, 11/5, 9/6, 18/1. As discovered by M Oehm, you can interpret the tops as 20s and the bottoms as 1s to get six perfect square numbers (except one which is off by 10, presumably a mistake). Taking their square roots gives LEMONS.

Answer 2

Building on Deusovi's answer: The Mayan numerals of the fourth door are stacked, to top being twenties, the bottom ones, yielding:

144 25 169 225 186 361

These are perfect squares (where 186 should be 196) and their roots are:

12 5 13 15 14 19

or, in letters:

LEMONS

Answer 3

The first one is

never

because

this

The second is

hold

because

each "Y" symbol is 1 and each "eye" symbol (<) is a 10, so you have 8 15 12 4 as results of those equations

The third

drugged

was solved in another answer, so working on the fourth one.

Answer 4

Adding onto what people have, the second is

HOLD, converting the cuneiform on the right to numbers (8, 15, 12, 4) and converting those to letters gives you "hold".

And given the other answers and the context of the story, I can assume that the last word will be

LEMONS, but I don't know why yet.