Hello!
Honestly I do not think it is necessary to use all of those security software at once (I am excluding Adguard from that opinion - I recommend you keep it regardless of which main security software you have).
I would stick to using Kaspersky Internet Security and Zemana Anti-Logger OR Kaspersky Internet Security and HitmanPro.Alert; if I had to choose between ZAL or HMP.A I would most likely choose HMP.A since it has a wider feature-set (e.g. exploit mitigation (it even supports BadUSB protection), ransomware mitigation, browser compromise protection (e.g. scans for unwanted hooks which may be from malware to steal passwords), etc).
Regarding compatibility issues, there may be on the keylogger protection side, but it is best for you to test it out yourself; make sure you have a backup say on case there is a problem which causes data corruption/loss.
That being said, regardless of which one you decide to use alongside Kaspersky Internet Security, you will be well-protected; please remember that no security can make you invincible and that it'll be down to you just as much as the protection installed and running on your system to keep yourself safe. That being said, as I said earlier, I do not think it is necessary to use both ZAL and HMP.A alongside KIS.
Stay safe and good luck.
