Why did Bilbo Baggins face change?
Also, why was Bilbo not affected by the ring?
According to Gandalf that is important. Sméagol was already not a good person, and the Ring affected him more because he acquired it by murder. Sméagol also used it to do bad things, while Bilbo rarely used it except to get away from annoying relatives. Sméagol also had it for nearly 500 years before he lost it.
Secondly, why was Bilbo so old?
Bilbo seems to have aged some after he gives the ring up to Frodo (he tells Frodo, "I am getting old"), but it isn't until the Ring is destroyed that his age really catches up to him. Gollum had the Ring much longer than Bilbo, so its hold on him, including its effect on his lifespan, was stronger.
Bilbo killed a few by throwing stones at them and by stabbing them with Sting. The spiders never found him, since during this time Bilbo made use of the Ring to remain invisible. After freeing the dwarves, he led them into a charge against the spiders, where the company killed dozens of the arachnids.