Hello,
chalisha means a prayer consisting of 40 verses (dohas). imilarly ashtak means prayers that contains 8 verses. Shruti is a kind of vedik heritage passed by earlier generations through oral traditions (guru teaches to student and student teached to next generation of students, and it continue.)
You can find hanuman kavach and hanuman baan/bajarang baan online. If you are serious about this, you can start reciting hanuman chalisa daily. If you have time and inclination you may opt to recite hanuman chalisa 11 times, it is very a very powerful prayer. Another way to worship hanumanji is by reading sundar kaand. Also, you can visit hanuman temple and offer your prayers by offering oil, udad daal, etc. Hanumanji loves raam-naam, so reciting raam-raksha, or shriram mantras are also a very good way to please hanumanji.
hope this helps.
JAI SHRIAM.