Linux Mint failed to install in UEFI mode

Let me try to answer this with a bit more background and formatting than in comments.

When a computer boots it needs to start somewhere. It needs some kind of instructions. For some CPU's that means reading the highest adress bits they can access and starting to execute a program from that adress (e.g. 6502). Some use different mothods. But all need some well defined place where they get their instructions are start executing them.

These instructions are called the firmware.
Your washing machine has them (at least the modern ones).
Your phone has them.
Your computer has them.

For an IBM compatible PC (1980's this program provided Basic Input and output routines and was called the BIOS. It would check several things (like count memory), then look for devices marked bootable, read the bootloader from the first device and transfer execution to that.

This basically has not changed since the first 4.77MHz XTs up to pentiums. Other computers (e.g. Suns, Indy/SGI, Apple, nextstep, Alpha's, ...) used their own firmware. Often much much capable then the PCs'.

For some reason (backward compatability?) the default firmware for the PC stayed more or less the same across decades¹. That is good for compatability, but after several decades it was severely outdated.

For this reason the EFI standard was developed. It is much more capable. It is also quite different and basically incompatible with BIOS firmware. That is not sto say that it looks any different. BIOS firmware and EFI firmware can be as hard to tell appart as a petrol fueled car can be from a diesel fueled car.

Yet many keep calling the UEFI firmware and EFI BIOS. Which is akin to calling a car a 'diesel car which only runs on petrol and not on diesel'. It is wrong. Simply wrong. Sadly it is not uncommon either and many big names are using it, probably because it sounds more familiar to the layman who called a firmware a BIOS, even when it is something completely different.

So now we live in a world with diesel only powered petrol car. :-(

Now to show a few of the differences:

• BIOS uses interupt calls for a lot of things.
• BIOS always supports MBR partitioned disks.
• BIOS boots from a bootsector (special code in aspecial place) on an MBR formatted disk.
• MBR format only allows for 4 primary partitions (plenty in the time if 5MB harddisk, but lacking in modern times)².

As for EFI (and UEFI)

• It has many more options which are not compatible with the was the BIOS firmware did things.
• It always supports GPT formatted disks.
• GPT formatted disks can have many partitions. One of those is usually the EFI system partition (ESP).
• EFI firmware can look on the ESP for a file to boot from. This file can be specific in NVRAM. If it is not present it will fall back to defaults, like ESP:/EFI/Boot/BootX86.EFI.

Now to confuse things.

Since there was a long period where BIOS was the standard and EFI was new many EFO firmware programs incorporated something called CSM (Compatability Shims). If you enabled these they would not only accept proper EFI calls but also to to resolve old BIOS style calls.

It still is a EFI though.

In other words: It still is a diesel car which runs best on diesel but which will not explode if you add petrol.

Add to this the habit of people mixing up the names and you can confusion gallore.

Ok, now on to your question:

I've got new Acer Aspire ES 15 with InsydeH20 bios

OK, this BIOS is not a BIOS. It is EFI.

I'm going to setup dual boot with Windows 10 and Linux Mint.

How did you install windows 10. I am assuming that you installed it in EFI mode. Which means that you also want to install mint in EFI mode.

Do not enable CSM or a protective MBR. This will only confuse matters.

I successfully installed Windows but Linux setup hangs when grub starting to install.

Grub supports both BIOS and EFI. Do you have an ESP with a grub.efi file?

Sadly I will leave your answer open here since I have no idea what is going on. Secure boot is an EFI feature will will check .EFI binaries before trying to boot them. No idea what setting a password has to do with that though.

I think, it's because of UEFI boot mode enabled in BIOS. But boot mode selector is inactive (can't open switch menu). Now I'm disabled Secure Boot which became available only when I've setted up the supervisor password. Boot Mode is unchangable yet

¹: More or less since PnP got added since late ISA. PCI enumeration, etc etc.

²: One of the changes to modern BIOS firmware is to understand extended partitions. Still limited though.