Are there any known issue with PHP 7.4.X?

I experience some navigation problems if logged in as admin. Not all links work as expected and don't lead to the desired page (nothing happesn if clocked).

Tried with Chrome 81 and FF 76.0.1

Only the github master 52rc is certified for php 7.4.  But You can switch 'display errors' on - and also makes entries in the gpconfig.php, if You want to look for errors. (Sometimes a Javascript-blocker can cause strange effects.) The clean solution is only the update. You can at first make a new installation in a subdomain and see, if You still experience errors.

Is there a planned release date of the upcoming V5.2?

Will 5.1 still work with PHP 7.3 until then?

Only the developers decide when 5.2 comes out, which will not be very different from momentary 5.2rc. Version 5.1 has minor bugs - thats one of the reasons  why 5.1 CE was developed (php 7.3).

Normally an exchange of the include-directory (and rename  the old 'include' before to include.old - together with a previous backup under 'tools')   will update the CMS - if it is not damaged.