I don't know if I resolve all problems but I describe what I found.

It seems MDButton works different than other widgets.

Here is original MDButton.__init__

    def __init__(self, *args, **kwargs):
        super().__init__(*args, **kwargs)
        Clock.schedule_once(self.adjust_width, 0.2)
        Clock.schedule_once(self.adjust_pos, 0.2)

It uses Clock to run self.adjust_width after 0.2 seconds to create button with minimal width - so it doesn't allow to use self.width at once in own __init__ because it will be replaced by width calculated in self.adjust_width

(by the way: as I remember __init__ can't calculate it directly because Kivy creates real objects later, sets values from files .kv, and after that code can change sizes - and this is why it has to use Clock to run code later)

I see two methods for this:

1. use also Clock to run own function which will change width little later

from kivy.clock import Clock

class mkbtn(MDButton):
    def __init__(...):

        # ... code ...

        Clock.schedule_once(self.update_later, 0.2)

    def update_later(self, args):
        self.width = dp(120)

2. replace adjust_width with own function - empty code - and it will not calculate own width

class mkbtn(MDButton):
    def __init__(...):

        # ... code ...

        self.width = dp(120)

    def adjust_width(self, args):
        pass

Result on desktop Linux

I also centered text on button (but text+icon may need different method)

#from kivy.clock import Clock

# if you put this before class mkbtn then you can use `func=dummy_func`
def dummy_func(x="", y=""):
    pass


class mkbtn(MDButton):
    def __init__(
        self,
        text,
        style="elevated",  #
        radius=[20, 20, 20, 20],
        icon=None,
        # func=lambda x: dummy_func(x),
        func=dummy_func,
        **kwargs
    ):

        super().__init__(**kwargs)
        self.style = style
        self.radius = radius
        self.size_hint_x = None

        # self.adaptive_width=True
        # self.size_hint_min_x = 0.3
        # self.wide = dp(120)
        self.width = dp(120)

        if icon:
            self.add_widget(MDButtonIcon(icon))
        self.add_widget(MDButtonText(text=text))
        self.bind(on_release=func)

        # center text on button - has to be after `add_widget(MDButtonText(..>))`
        self._button_text.pos_hint = {"center_x": 0.5, "center_y": 0.5}

        # center button 
        # self.pos_hint = {"center_x": 0.5, "center_y": 0.5}  # center Y

        # Clock.schedule_once(self.update_later, 0.2)

    # def update_later(self, args):
    #    self.width = dp(120)

    def adjust_width(self, args):
        pass

---

If in Button and TextField you use pos_hint = {"cente_y": 0.5} then both widgets will looks like in one line.

#from kivy.clock import Clock


class TxtField(MDTextField):
    def __init__(self, ilen=7, htxt="", shintx=0.7, **kwargs):
        super().__init__(**kwargs)
        self.mode = "outlined"  # "filled"
        self.size_hint_x = 0.5

        # center textfield in layout (Box)
        self.pos_hint = {"center_x": 0.5, "center_y": 0.5}  # center Y

        self.input_filter = lambda s, u: (
            s if (len(self.text) < ilen and s.isdigit()) else ""
        )

        if not htxt:
            htxt = "input:"

        self.add_widget(MDTextFieldHintText(text=htxt))


# if you put this before class mkbtn then you can use `func=dummy_func`
def dummy_func(x="", y=""):
    pass


class mkbtn(MDButton):
    def __init__(
        self,
        text,
        style="elevated",  #
        radius=[20, 20, 20, 20],
        icon=None,
        # func=lambda x: dummy_func(x),
        func=dummy_func,
        **kwargs
    ):

        super().__init__(**kwargs)
        self.style = style
        self.radius = radius
        self.size_hint_x = None

        # self.adaptive_width=True
        # self.size_hint_min_x = 0.3
        # self.wide = dp(120)
        self.width = dp(120)

        if icon:
            self.add_widget(MDButtonIcon(icon))
        self.add_widget(MDButtonText(text=text))
        self.bind(on_release=func)

        # center text on button - has to be after `add_widget(MDButtonText(..>))`
        self._button_text.pos_hint = {"center_x": 0.5, "center_y": 0.5}

        # center button in layout (Box)
        self.pos_hint = {"center_x": 0.5, "center_y": 0.5}  # center Y

        # Clock.schedule_once(self.update_later, 0.2)

    # def update_later(self, args):
    #    self.width = dp(120)

    def adjust_width(self, args):
        pass

---

If you add background color in MDBoxLayout then you see how it is centered

        self.hlay5 = MDBoxLayout(
            orientation="horizontal",
            padding=[5, 5, 5, 5],
            spacing=dp(10),
            md_bg_color=[1, 0, 0, 1],
        )

Before centering:

After centering:

---

To reduce height in rows I have to use size_hint_y=None in every hlay* and bind function which will calculates minimal height for every hlay*

self.hlay4.bind(minimum_height=self.hlay4.setter("height"))

class MainScreen(MDScreen):
    def __init__(self, **kwargs):
        super().__init__(**kwargs)

        self.md_bg_color = [1, 1, 1, 1]
        # md_bg_color: self.theme_cls.secondaryContainerColor

        self.main_layout = MDBoxLayout(orientation="vertical")

        self.app_bar = MDTopAppBar(type="small")
        self.abtitle = MDTopAppBarTitle(
            text="WOS Squad Ratio (Bear/CJ)", halign="center"
        )
        self.app_bar.add_widget(self.abtitle)

        self.content_layout = MDBoxLayout(
            orientation="vertical",
            padding=[5, 5, 5, 5],
            spacing=dp(10),
        )

        self.hlay1 = MDBoxLayout(
            orientation="horizontal",
            padding=[5, 5, 5, 5],
            spacing=dp(10),
            size_hint_y=None,
        )
        self.bdctf = TxtField(htxt="Bear DC", ilen=6)
        self.prof_btn = mkbtn("Profiles", icon="triangle-small-down")
        self.hlay1.add_widget(self.bdctf)
        self.hlay1.add_widget(self.prof_btn)
        self.hlay1.bind(minimum_height=self.hlay1.setter("height"))

        ###
        self.hlay2 = MDBoxLayout(
            orientation="horizontal",
            padding=[5, 5, 5, 5],
            spacing=dp(10),
            size_hint_y=None,
        )
        self.cdctf = TxtField(htxt="CJ DC", ilen=6)
        self.aprof_btn = mkbtn("Add Profiles")
        self.hlay2.add_widget(self.cdctf)
        self.hlay2.add_widget(self.aprof_btn)
        self.hlay2.bind(minimum_height=self.hlay2.setter("height"))

        ###
        self.hlay3 = MDBoxLayout(
            orientation="horizontal",
            padding=[5, 5, 5, 5],
            spacing=dp(10),
            size_hint_y=None,
        )
        self.titf = TxtField(htxt="Total Infantry", ilen=7)
        self.cb_btn = mkbtn("Calc Bear")
        self.hlay3.add_widget(self.titf)
        self.hlay3.add_widget(self.cb_btn)
        self.hlay3.bind(minimum_height=self.hlay3.setter("height"))

        ###
        self.hlay4 = MDBoxLayout(
            orientation="horizontal",
            padding=[5, 5, 5, 5],
            spacing=dp(10),
            size_hint_y=None,
        )
        self.tltf = TxtField(htxt="Total Lancer", ilen=7)
        self.cc_btn = mkbtn("Calc CJ")
        self.hlay4.add_widget(self.tltf)
        self.hlay4.add_widget(self.cc_btn)
        self.hlay4.bind(minimum_height=self.hlay4.setter("height"))

        ###
        self.hlay5 = MDBoxLayout(
            orientation="horizontal",
            padding=[5, 5, 5, 5],
            spacing=dp(10),
            md_bg_color=[1, 0, 0, 1],
            size_hint_y=None,
        )
        self.tmtf = TxtField(htxt="Total Lancer", ilen=7)
        self.sd_btn = mkbtn("Save Data")
        self.hlay5.add_widget(self.tmtf)
        self.hlay5.add_widget(self.sd_btn)
        self.hlay5.bind(minimum_height=self.hlay5.setter("height"))

        ###
        self.tlbl = MDLabel(
            halign="left",
            role="large",
            padding=[5, 0, 0, 500],
            text="",
        )

        def cng_lbl(txt):
            self.tlbl.text = txt

        ###
        self.content_layout.add_widget(self.hlay1)
        self.content_layout.add_widget(self.hlay2)
        self.content_layout.add_widget(self.hlay3)
        self.content_layout.add_widget(self.hlay4)
        self.content_layout.add_widget(self.hlay5)
        self.content_layout.add_widget(
            MDWidget(
                # size_hint_y=1,  # doesn't need this
                md_bg_color=[0, 1, 0, 1],
            )
        )

        ###
        self.main_layout.add_widget(self.app_bar)
        self.main_layout.add_widget(self.content_layout)

        ###
        self.add_widget(self.main_layout)

It keeps sizes after resizing window.

but problem is when window is too small to keep all elements