A series of recent problems with new MacBook Pro

Question

Hi,
I bought a new MacBook Pro last May.  The spec is:
Retina, 13-inch, Late 2013
Processor: 2.4 GHz Intel Core i5
I installed Yosemite in November (I think) and the Mac has been giving problems ever since.  I'm not sure whether the problems are related to this installation, but I did not change anything else prior to the problems starting.
When I boot up my Mac, a message appears: "Finder was not shut down correctly. Reopen all windows from last session?" 
This is inaccurate since I shut down the Mac correctly every evening.
Safari used to load pages quickly, but now when I first open it, it takes about a minute to open a page.  Once it's running, it takes approximately 10 seconds to load a page.  The spinning beachball appears regularly and Safari often quits.
Mail Rules are also operating differently.  Whenever I created a new rule, prior to November, the rule would automatically have the name Rule [last rule + 1} i.e. if the last rule I created was Rule 41, the new rule would be called Rule 42.  However, now all rules are called Rule 2 (I know that I can change this).  This isn't a huge issue, I'm just mentioning it in case it helps to solve the problem.
Another occasional problem that has happened approximately three times is that applications freeze.  I can still move the cursor around the screen but I cannot click on anything or take an action within an application.
I would be grateful if you could advise me on this, please.
Many thanks,
F.

Answer 1

Your computer is insured for one year from date of purchase. You paid for that coverage.
If at all possible take your computer to an Apple store and have a "genius" look at it.
You should make an appointment: google "Apple genius bar appointment" and proceed from there.