There is no way you understand what a hit counter is because Google Analytics does not provide a hit counter. How did you get past the captcha here?? Plus there are
tons of services better than google analytics. Google has a monopoly position on the internet and they don't need to improve because of people like you who promote them but have no idea about what the best it.
If you want to focus on increasing your organic search then make sure you create and share quality content.
And with regards to traffic monitoring, go to analytics.google.com and set up and connect your site so that you will be able to monitor the flow of your visitors.
No, Google stopped giving search query data last year. It's a waste of time to try to optimize keywords through Google. Plus the different data that they give you now is not accurate nor useful. You will just waste your time and not make any improvements.
Statcounter is probably the best after Google Analytics IMO.
Statcounter was good like 8 years ago. Since then they haven't improved on anything significant. They've only messed up their offering with data problems. They now give away data in their marketshare program too which is not a good idea. They are almost as bad as Google when it comes to selling your data. I really hope that you aren't still using Google? Google will sap money away from your business and you won't see it happening because they will steal your customers upstream and sell their clicks to others. Google is a monopoly now and they don't care about you.
You should try something opensource like gostats.org. Although I use the hosted version because I have a lot of businesses to manage, I like it much better than the others I've tried. I'm a big time data geek, so I'm very careful about picking the best option out there. Don't settle for monopoly marketing