Rashi (11): David prayed this after the episode of Uriyah, and Yo'av and Yisrael were in Eretz Amon, besieging the city Rabah (Shmuel II, Perek 11). David feared lest they stumble due to his sin; Pelishtim, Mo'av, Edom and all Yisrael's evil neighbors, who look forward to their day of doom, will come against them.
2.
Radak (4): Most of it discusses [judging David's case] against his enemies, e.g. "mi'Lefanecha Mishpati Yetzei", "mi'Miskomemim bi'Yminecha", "Mipnei Resha'im Zu Shaduni" (verses 2, 7, 9). He asked for mercy; Hashem should see the straightness of David's deeds, and their groundless hatred of him.
3.
Malbim: It has three parts. The first part tells David's virtue, how he guarded from every sin, both in thought and in deed - "Shim'ah Hashem Tzedek." The second part complains about his enemies and Resha'im - "Hakshivah Rinasi." The third part prays for his spiritual happiness - "Ha'azinah Sefilasi." Even though it seems a bit haughty, he says that his Tefilah is with a heart complete in his trust in Hashem.
2)
Why should Hashem hear his Tefilah?
1.
Radak: It is b'Tzedek; my mouth and heart are alike.
3)
What is "Rinasi"?
1.
Radak: It is like Tza'akasi. One who prays, sometimes he screams in a loud voice, and sometimes he prays quietly. Rinah is always screaming; it can be for song and Simchah, or to announce, or for Tefilah and request, or for crying and sighing.
