I have no idea how do mage survive at start out level like if I wanted to focus on Conjuration and Alteration with Restoration as sub skill, how do I even do that when I don't even have any spell except destruction spell at level 1?
If you choose a Breton as your mage, then you start out with one Conjuration spell (Summon Familiar). That's a start.
Also, do mage had to wear ropes or they can do light armor?
Ropes? No... you can wear robes instead, if you wished.

There's no restrictions on what you can and cannot wear. If you wanted to blast fireballs from your fingertips while wearing heavy plate armor, you can... without penalties.
I was also wondering that how do mage obtain more powerful spell like how do I go from novice to master spell ? I know that I have to use spell for that specific skill in order for it to level up but does it go from novice to apprentice by it self or u have to buy something like spell books from those mages at the college?
As you gain levels in a particular skill, the spell book merchants will start to open up more powerful spells to purchase. You don't even have to have the Adept perk in order to see Adept level spells in the list of purchasable spell books. I've seen the Fireball spell available when I had the Apprentice level Destruction perk.
And you can not only purchase spells from the mages at the College of Winterhold, the court wizards also have spells available for purchase... though, they don't carry a wider selection than the College.