Software

I recommend you to use a freeware called Format Factory, it supports MKV and other video/audio/image formats.
Believe me, it's really 100% free and no ads.
(link removed by moderator)

As I know, there are lots of free and online video converters in the market that you can use, like onlinevideoconverter, any video converter, etc. If you don't mind low-budget, I think you can use Joyoshare Video Converter. It converts with 60X fast speed and supports multi-subtitle, muti-track videos. I also use it to convert audios, DVDs, live photos. Fast and lossless!

I think VLC media player could solve this. There is an inbuilt video converter in this software. And VLC is totally free.

Maybe you can try to convert MKV to MP4 using some online converters, such as Zamzar, Convertio. They are free and easy to use. However, if your MKV files are large you can try Joyoshare Video Converter. It can convert them without quality loss. Also, VLC is a good option to encode video.

some suggestions are really nice, but are these converters still actual?

I know how frustrating it can be...especially the need to make several conversions pisses me of. I think the easiest is to find a free tool that would convert this type of files. I think I also read somewhere that VLC could solve this, but I am not sure. Anyway, if you find a great service, share it here)))
Johan, yes people still do this surprisingly or? Sometimes I need it for my job, or I am pretty sure that not everyone has access to modern tools that make the converters already nonsense. So it is actual, even now)

Recommendation of a Youtube mp3 converter removed by moderator.