What is the meaning of "Askilah"?
Rashi: I will put my heart to [Radak - understand] the way of the pure.
Malbim: I will test whether I am truly pure. Refer to 101:2:2:1.
What is "Tam"?
Malbim: He does virtuous acts not for any side motive, e.g. hope for reward, fear of punishment or another reason, e.g. to be haughty and glorify himself. Rather, it is due to love of good because it is good, and Hashem commanded about it. In a broader sense, one who appears to always do Tzedek and never veers from it is called Tam, even though perhaps in his heart he is not Tam, for he has other motives for doing Tzedek. To distinguish, the former is called Tam Levav; purity is rooted in his heart.
What is the meaning of "Masai Tavo Elai"?
Rashi: The straight path to go on it - when will it come to me [Radak - via Ru'ach ha'Kodesh]?
Malbim: I will not go on the straight path amidst habit, rather, it will be planted in my heart.
Why did he say "b'Kerev Beisi"?
Rashi: I will go in the purity of my heart, and even covertly in my house, like in public.
Radak: This is like one who puts all his heart to think about a matter. He goes in his house, one [step] here and one here. So it says about Elisha - "va'Yelech ba'Bayis Achas Henah v'Achas Henah" (Melachim II, 4:35).
Malbim: This is where I can test my purity - if it is even where there are no other motives of [receiving] praise or glory (others do not see me). Before (verse 1) it mentions Chesed and Mishpat, for they are equal for a Tam (he is pleased with both of them).