Media Queries Running Weird Because of Non-Integer Width

How can I avoid media query overlap?

The only reliable way to create two mutually exclusive @media blocks for any given media query is to use not to negate it in one of the blocks. Unfortunately, this means repeating your media query once for each @media block. So, instead of this for example:

@media (max-width: 49.9375em) {
    body {
        color: red;
    }
}

@media (min-width: 50em) {
    body {
        font-size: larger;
    }
}

You would have this:

/* 
 * Note: Media Queries 4 still requires 'not' to be followed by a
 * media type (e.g. 'all' or 'screen') for reasons I cannot comprehend.
 */
@media not all and (min-width: 50em) {
    body {
        color: red;
    }
}

@media (min-width: 50em) {
    body {
        font-size: larger;
    }
}

Interactive jsFiddle demo

This is very effective at closing the gap with range media features like width and height since it essentially turns this into an either-or scenario. But, like your first two options, it isn't perfect: as mentioned, you have to repeat the same media query twice, and add not to one of them. There is no if/else construct for @media as described in Conditional Rules 3.

Although I mention this in my answer to your previous question:

From my experiments it would seem Safari on iOS rounds all fractional pixel values to ensure that either one of max-width: 799px and min-width: 800px will match, even if the viewport is really 799.5px (which apparently matches the former).

It should be noted, still, that I've noticed some quirks when it comes to rounding. That said, I haven't been able to find a fractional value that would evade both media queries and end up not receiving styles from either set of rules (which, by the way, is the worst that can happen, so don't worry about potentially creating a space-time rift). That must mean browsers — at least, Safari as I've tested — do a reasonable job of ensuring they satisfy media queries even if you have values that differ (by exactly 1 CSS pixel).

When it comes to units with larger gaps that can be observed on desktop browsers, though, like ems, there is a much larger margin of error. For example, one comment suggests using 49.99999em instead of something more arbitrary than 49.9375em, but apparently there is a difference, at least with a default font size of 16px.

I simplified your code, changed the media queries to use decimal values, and put the code in jsFiddle:

@media (max-width: 49.9375em) {
    body {
        color: red;
    }
}

@media (min-width: 50em) {
    body {
        font-size: larger;
    }
}

If you resize the Result pane to exactly 800 pixels (the text will update to guide you along), you actually end up with different results depending on whether @media (max-width: 49.9375em) is used, or @media (max-width: 49.99999em) is used (I was surprised by this too)...

Either way, you're right: option 2 has its drawbacks too. I'm not particularly fond of it, to be honest, because I wouldn't want to crack my head over device and user agent quirks which are out of my control. If you're like me, I suppose it would be better to go through the inconvenience of redeclaring your rules at the cost (?) of being more vigilant around your code, as that's at least still within your control as an author.

Why does Bootstrap use a 0.02px difference between screen size thresholds in its media queries?

There isn't a good way to make two px-based @media rules mutually exclusive with no gap without repeating the same media query twice and using the not keyword — which isn't very readable much less DRY — and the < and > syntax new to Media Queries 4 isn't widely supported yet. As you've seen in my answer to the linked question, a viewport that is (in this example) exactly 576px wide will match both max-width: 576px and min-width: 576px simultaneously, which can cause issues (some cascading some not) as properties from both rules will be applied. Most authors therefore choose to have min- and max- constraints with a difference of 1 pixel, or less if they're worried about high-resolution displays with non-integer pixel densities that don't scale every CSS pixel to full device pixels (e.g. 1.5).

Indeed, cross-browser compatibility is the reason: according to Bootstrap's source, 0.02px is used "rather than 0.01px to work around a current rounding bug in Safari. See https://bugs.webkit.org/show_bug.cgi?id=178261" (that, predictably, as of July 2018 still hasn't been fixed). Starting from line 31 of _breakpoints.scss:

// Maximum breakpoint width. Null for the largest (last) breakpoint.
// The maximum value is calculated as the minimum of the next one less 0.02px
// to work around the limitations of `min-` and `max-` prefixes and viewports with fractional widths.
// See https://www.w3.org/TR/mediaqueries-4/#mq-min-max
// Uses 0.02px rather than 0.01px to work around a current rounding bug in Safari.
// See https://bugs.webkit.org/show_bug.cgi?id=178261
//
//    >> breakpoint-max(sm, (xs: 0, sm: 576px, md: 768px, lg: 992px, xl: 1200px))
//    767.98px
@function breakpoint-max($name, $breakpoints: $grid-breakpoints) {
  $next: breakpoint-next($name, $breakpoints);
  @return if($next, breakpoint-min($next, $breakpoints) - .02px, null);
}

@media not working with width less than 1024px

Every rule in CSS is able to override any previous rule to the same selector. So you just need to switch your code in order to get it working:

@media (max-width: 1023.9px) {
  width: 33.3333%;
}

// experimental
@media (max-width: 1000px) {
  width: 50%;
}

@media (max-width: 768px) {
  width: 50%;
}

@media (max-width: 599px) {
  width: 100%;
}

//
@media (min-width: 1024px) {
  width: 25%;
}

The reason why your rules override each other is because they all have the same selector and while max-width: 599px is accurate and correct, the later appearing max-width: 1023.9px is it, too and thus it’s overriding the previous width: 100%; from the max-width: 599px media query.

And a side note here: Use integer values only for media queries. There is no screen in the world, which has .9 or even .5 pixels.

the 1px gap when using min and max with media queries

Because you have the same breakpoint for min/max-width.

That's why when min-width is used it's added a pixel or other way around subtracting a pixel to max-width.

With this in mind, you have 2 options:

First

@media (min-width: 769px) {
.test2{
    display: block;
  }
}
@media (max-width: 768px) {
  .test1{
    display: block;
  }
}

Second

@media (min-width: 768px) {
.test2{
    display: block;
  }
}
@media (max-width: 767px) {
  .test1{
    display: block;
  }
}

You can read about media queries order matters?

How to use or (Greater than and Less than ) Symbols in Media Queries

Media queries don't make use of those symbols. Instead, they use the min- and max- prefixes. This is covered in the spec:

Most media features accept optional ‘min-’ or ‘max-’ prefixes to express "greater or equal to" and "smaller or equal to" constraints. This syntax is used to avoid "<" and ">" characters which may conflict with HTML and XML. Those media features that accept prefixes will most often be used with prefixes, but can also be used alone.

So, instead of something like (width <= 768px), you would say (max-width: 768px) instead:

@media screen and (max-width: 768px) {}