It should be possible to use a 386DX at 25mhz without any changes. Else you need to look at the motherboard and see if there is some kind of frequency control, back then the cpu/chipset speed was set most of the time to a single working clock. Some later boards had the ability to change speed via jumper settings though.
Since this has a 386sx cpu there is a high chance it does not have any cache - something that will kill speed even if you install a 386DX. IMHO it's more important to have cache than upgrade to a DX cpu.

If it's really an SX, you can not replace it with a DX (unlike with the 486), since the SX has less pins and using a mainboard based on 286 technology.

By the photos it's 386DX system. Might be 16MHz as there is a 32MHz oscillator near cpu.

So if is the 386DX? Can be upgraded? To DX40 or even DX33?

Once again it depends on whether the motherboard has frequency control or not , there is no way to tell without model number or better photos.
It looks like a really old mobo so I doubt you can raise the clock without issues.

Also try to find out if it has cache, I had a cacheless 386DX/20 and the speed difference from a 286/16 wasn't great in games, maybe 1fps or something in Wolfenstein3D for example.

I asked the seller to send me a better quality picture of the cpu.

I found also a board with a 386DX40, 8mb RAM and math coprocessor installed.

What do you think?

I remember seeing that ad at some point - that's a pc made by intel themselves and branded as ergodata. Ask the seller for a better pic of the intel sticker at the back: it will have a model and from then you can know everything for that pc. It comes with MDA adapter so you can bet it's one of the first 386 PCs made.

The 386DX40 mobo is a nice and typical one, 128kb cache is under the ram, fpu present, battery looks good, UMC chipset. Go for it.

And get that barrel battery out of there as soon as it arrives.

It appears that system has two proprietary memory cards installed, in addition to the 8 SIMM slots which are filled.

Judging by the age of the board, I would guess a 20 or 25MHz CPU swap should be possible if you swap out the CPU crystal as well. 33MHz is a big maybe. 40MHz is a big no.

Thank you everyone. I bought the first complete 386 board I mentioned earlier.

I need to find an AT desktop case with PSU to complete the build up.

Awesome