What is "Tishm'ru es Kehunaschem" referring to?
Seforno: It is a warning to Kohanim not to permit Zarim to perform the Kehunah. 1
What are the implications of "Avodas Matanah"?
Rashi: It impliesthat Hashem gave the Avodah to the Kohanim as a gift. 1
Ramban and Targum Yonasan: The Torah is teaching us here that the Avodas ha'Kehunah is not an onus, like the service of human kings, but a (precious) gift, which Hashem personally gave to the Kohanim for honor and glory. 2
Seforno: It implies that the Kehunah is seen by everyone as a badge of honor, which they envy and which therefore needs to be carefully guarded.
Targum Yonasan: It teaches us that the Kohanim serve by drawing lots, like one distributes a gift, 3 anD that eating the Korbanos is compared to bringing them on the Mizbe'ach.
Yoma, 24a: It implies to preclude ffrom the Chiyuv Misah a. "Avodas Matanah", 've'Lo Avodas Siluk' (an Avodah that entails removing) - a Zar who performs the T'rumas ha'Deshen and one who performs the Dishun Mizb'ach ha'Penimi and the Dishun Menorah and b. "Avodas Matanah", 've'Lo Avodah he'Yesh Acharehah Avodah' (an Avodah that requires another Avodah after it) - a Zar who performs Kabalas ha'Dam and Holachas ha'Dam. 4
Rashi probably means 'and no as a burden - like the Ramban in answer #2.
Ramban: As the Gemara says in Sotah, 15a, commenting on Pasuk 8 (in connection with eating the Korbanos) "le'Mashchah" - 'for greatness; the way that royalty eats'.
Yoma, 24a: And he is Chayav for performing Zerikas ha'Dam, Nisuch ha'Yayin and Nisuch ha'Mayim, and for the seven sprinklings in the Heichal of the Par He'elam Davar, the Par Kohen ha'Mashi'ach and of the bull and the goat of Yom Kipur - which we learn from "le'Chol D'var ha'Mizbe'ach". See Torah Temimah, citing Yoma (Ibid.) and note 12.
What is the gist of Hashem's answer to the people's concern, bearing in mind that a Zar is still Chayav Misah for coming close and the Levi'im were already commanded to distance them (See 1:53, 3:9-10 & 8:19)?
Rashbam (on Pesukim 1 & 7): In answer to Yisrael's complaint, 1 a. Hashem now placed on them a Chiyuv Misah for entering the Mishkan, 2 and b. He ordered the Kohanim exclusively to perform the Avodah, thereby ensuring that not only will Yisrael be afraid to come close, but that they will also have no reason to come close.
Moshav Zekenim (on Pasuk 28, citing the Riva): Above (on 8:19) the Torah write "ve'Lo Yih'yeh bahem Negef," implying that if even if one Yisrael approaches, there will be a plague among all Yisrael. When Korach approached the Avodah, Hashem said "Hibadlu mi'Toch ha'Eidah", and Moshe said, 'will You be angry with everyone due to one person?!' (16:21 & 22), there is a P'sik between "Kol" and "ha'Karev" 3 (17:28)
Which Misah does the Zar receive?