answer to question 2 had some mistakes this is correct:
2) “Why can’t Chanukah start on Tuesday?”
for Chanuka to start on Tuesday You would need Rosh Hashana on Tuesday and the year “shalem” meaning that cheshvan and Kislev both have 30 days* In such a year 1 Kislev would be Shabbos 22 Kislev would be 3 week late on Shabbos, 23 sunday, 24 Monday 25 Tuesday.
However such a year is impossible a shalem year has 355 days if regular and 385 days for leap year
For a regular year Rosh Hashana would occur 355 days later ie 50 weeks and 5 days, which means Rosh Hashana would be Sunday – an impossibility
For a leap year Rosh Hashana would occur 385 days later ie after exactly 55 weeks. That would mean Rosh Hashana on Tuesday, while this is THEORETICLY possible, in reality it isnt becasue 2 Tuesdays back to back are impossible see Question 1
*It doesn’t matter how many days Kiselv has for this , but the choices are 29 for both Cheshvan and Kislev 29 for Cheshvan and 30 for Kislev or 30 for both. there is no possibility of 30 for Cheshvan and 29 for Kislev