The following website goes into details on how to use a penny to verify if your tires have a legal and safe amount of tread. http://www.reviewsonline.com/auto/TT03-1.htm
No the rims do not need to be replaced along with the new tires unless certain conditions require you to do so. The only time you need to replace the rims along with the tires are when you damage or lose them.
new tires. If the tires brake, you'll need it
You can shop and purchase the snow tires you need for your car at treaddepot.com/Tires. They offer free Shipping on All Cooper & Toyo Winter Tires. Limited Time Only!
If the tires are starting to look bald and warn then it is time to change them, your local garage will be able to tell you and give you an estimate on new tires
Yes the new tires are faster and do not slip.
Good idea to do at the same time
Practically no. By the time the studs are worn out, tires are too worn for you to install new studs and even if you could, the cost of replacing them would be more than the tires are worth.
Only aggressive tread new tires whine.
get a penny, and place it upside down (with Lincoln's head facing down) in one of the grooves. if you can see the top of the head its time to get new tires.
You could stick a lincoln penny in the tread. Having lincoln's head facing away from you, if it doesnt cover any of the top of the head it's time for new tires
If everything was fine prior to the new tires and If the tires were balanced correctly then you have at least 1 defective tire rotate the tires to identify where the culpret is.
Not necessarily. If the car was in alignment prior to getting the new tires, it will be in alignment after the new tires. It isn't a bad idea to check the alignment periodically and it is probably better to check it more frequently than when you get new tires.