1, 2) Or Hachayim to 10:7 explains that their hearts were still hard, and they wanted to just allow the Jews to take a short trip for a few days to serve their God in a way that they would certainly return. In his understanding, the fact that they thought that simply letting them have their way for a 3 day vacation would fix everything is the part that shows that their heart was still hardened, and in fact, Or Hachaim says that when Moshe asked to take everyone with (i.e. no guarantee that they would return) the slaves also agreed with his refusal:
עד מתי יהי׳ וגו׳ – לא שהסכימו לשלח ישראל בהחלט כי הנבואה שאמר ה׳ למשה הכבדתי וגו׳ תכחיש זה אלא שרצו שילכו באופן שיחזרו ודאי ולזה תמצא כשאמר משה בנערינו ובזקנינו וגו׳ וגרש׳ פרעה לא יספו דבר עוד בדבר הזה גם פיהם ענה בם כי לא האמינו בסדר המעשה כי אלהי העברים הגדול הגבור והנורא נטה ידו בהם לשלוח ישראל אלא שהיו יוקשים בהם ואין לך כפירה באמיתות הענין כזה.
Ibn Ezra to Shemos 10:1 explains that it was only up until now that Hashem had hardened Pharaoh's servants hearts (and that was the reason why they did not send them out during/after Barad, see for example, Rashbam and others). However, now that Moshe had come forward threatening Arbeh, they snapped to their senses, and were softened. (Note that he mentions this issue directly in his second Perush there.)
Chizkuni (10:7, above link) says that the hardening of the hearts was that they only wanted to send out the men (Shalach es Haanashim), and not everybody:
ויאמרו עבדי פרעה אליו – ומה שכתוב למעלה הוא ועבדיו הם אותם שהשיאו עצה שלא לשלח רק את הגברים.
3) Ibn Caspi to 10:1 and 10:7 (above links) says that Avadim here means his top, honorable advisors and officers. I would assume that this is what others take for granted. (Note that the Avadim are involved throughout the entire story, during the Maakos, and even when the snake/staff trick was performed, amking this very likely.) Edit: Malbim to Bereishis 20:40 says this as well.
Another possibility is that it refers to a large portion of Egypt's population, and that the populace, even though they were slaves to the king, still had a say. Pharaoh perhaps feared an uprising from them as well.