Maybe I can help you.
First: You can rescale the HUD in your settings in "Interface" I think. The Mini Map and Chat size can be rescaled separately. I have my HUD rather small and bumped up my Mini Map to "100". You do as you want but if you struggle with how to adjust it, here's how I do it.
Second: League has added a "Camera Lock Setting" a couple of months ago and you can choose between "Fixed Offset" (camera locked to have your champion in the middle of the screen), "Per Side Offset" (camera locked to have your champion adjusted to the side of the map you're playing, i.e. blue side= champion in the bottom left corner; red side= champion in the top right corner) and then there is "Semi-Locked" (This lets you move your map freely until your champion collides with one of the borders of your screen).
The problem with this one is that "Per-Side Offset" doesn't behave like it should since Patch 6.2 ... At the moment it is identical to "Fixed Offset" and it bothers me really hard as I always have "Per-Side Offset". I'm pretty sure this is the one you are looking for.
This issue is at the top of the bug reports for Riot already. So it will be fixed very soon.
Third: I have a keybind to the space bar for "Toggle camera lock". This lets you switch between locked and unlocked really easily. This is just a personal preference and it helps me work around the problem with "per-side offset" until it is fixed. I always used it like this because being unlocked permanently makes me lose control too often and being locked permanently basically keeps me from playing the game as I have no idea what's going on. You can try it and maybe you like it.