(someone) has come a long way

To "come a long way" means to grow or show improvement:

You're still not quite ready to compete, but you've come a long way.

You can tell someone that they have "come a long way" if you're their teacher, mentor, coach, etc.

since (some event)

"Since" is used to talk about something that has happened after a certain time in the past.

You use "since" with "have":

I've loved him since I was 10 years old.

Haven't you eaten anything since lunch?

You don't use "since" with simple past tense verbs. Remember this! For example, "I loved him since I was 10" isn't correct.

If you were just talking about a point in the past, you can say "since then":

I moved out of my parents' place in 2003, and since then I've lived in 6 different apartments.

I've (done something)

When you're talking about an experience that started in the past and is still continuing now, you use "I've ___":

I've studied karate for over 12 years.

You can also use "I've ___" for something that just finished:

I've been driving for the last 8 hours. I can't drive any more.