Hala hatırlayım. I still remember.

Hatırlmayım. I don´t remember. Thank youuuuuuuuuuuuuuuuuuuu

 hala hatırlıyorum

hatırlamiyorum

my try

Maybe you could use ´hala hatırladım´ and ´hatırlamadım´

(using the past tense for the present like when we say ´anladım´ and ´anlamadım´  

Hala hatırlarım / hatırlıyorum.

nope. you cannot use it like this.

when you have "hala" you cannot use simple past tense as it indicates something that still goes on (like present prefect). you should use simple present or continous

hala hatırlarım/hatırlıyorum

in case you hear it from someone you can also use "mişli geçmiş zaman"

hala hatırlıyormuş (it is said that he still remembers)

when you don´t use "hala", it is possible to say in past tense as you said like "anladım" "özledim" etc

so hatırlamadım is correct for I don´t remember, as well as hatırlamıyorum.