I understand that the public Torah reading is a mitzvah and therefore we recite a blessing upon it's public recitation. However, the haftarah is not a separate mitzvah. I learned that it was used in place of the public Torah reading during a time of persecution when Jews were not allowed to publicly read the Torah. So...
1) Why do we recite blessings on the Haftarah reading?
2) Why are both the Torah aliyah blessings and the haftarah blessings not formulated as "al mitzvat...."
Encyclopedia Yeudis says in the name of the Kalbo that there are 7 Brachos for the Haftora against the seven who had Aliyos. It says that the Brachos are mentioned in Mesechtas Sofrim 13.
המפטיר מברך שבע ברכות על ההפטרה נגד שבעה העולים לס"ת (כלבו) במס' סופרים (פי"ג) נרשמו הברכות שאומרים לפני ואחרי ההפטרה (ויש שינויים בסדור רב עמרם גאון), ומסיים "בא"י מקדש ישראל ויו"ט פלוני" חוץ משבת שאינו מזכיר בחתימה ישראל, אלא "מקדש השבת בלבד" (עי' פסחים קי"ז: אפטרתא מגן דוד).
Supplementing @GershonGold's answer, see this article. There is a controversy as to whether the brachot recited before the haftarah are really 1 or 2 brachot.
In response to your second question, there are a few reaons, all based on what I am inferring form the linked article.
Haftarah was originally considered supplemental to the Torah reading, if you view the history mentioned in this article . It was only later, that it temporarily became a substitute for the Torah reading. I'm surmising, then, that since it's "attached" to the Torah reading, it's not considered a "separate" mitzvah.
Citing excerpts from the linked article who quotes Avudraha"m:
First we say: Asher Bachar B’Nevim Tovim meaning that we are excluding false prophets.. Chazal decided to show honor to the Torah and to Moshe, teacher of all the Prophets and then added that G-d chose the Torah and Moshe his servant. In order not to make it appear that Moshe was being mentioned after the Prophets, Chazal began the second part of the Bracha with the word: Baruch but not to indicate that it was the beginning of a separate Bracha. If that was Chazal’s intention, Chazal would have closed with a Bracha and not opened with a Bracha. Since Chazal mention the Torah and Moshe they returned to mentioning the Prophets who were true and to mention what was above in a place below.
I'm surmising that the first words in the 1st bracha start with Asher Bachar which, while not indicating, directly, that it is a mitzvah to recite haftarah, seems to indirectly imply that since G-d chose truthful prophets whose words are no less important then those of Moshe in the Torah, in a sense, we are obliged to mention the words of the prophets as well as the words of the Torah.
