Hi Eugene,
Welcome to Quantopian!
1) If you're unfamiliar with Python, I'd recommend starting out with a Python tutorial. Here are a few good resources:
http://www.codecademy.com/tracks/python
https://docs.python.org/2/tutorial/
http://www.diveintopython.net/
http://www.learnpython.org/
After that, the Getting Started Tutorial is the best way to learn the basics of the Quantopian API.
2) I'm not sure I understand this question entirely. Are you asking if you need to write any of the code to interact with your broker? If so, the answer is no. You only have to write your strategy.
3) Yes. However, algorithms can only place trades during market hours (9:30AM-4:00PM ET Mon-Fri). No need to buy server space.
4) You cannot see operation logs between Quantopian and IB, but you can see the transaction history when you live trade an algorithm. You can also add custom logging to your algorithm.
5) Quantopian is free to use. The only costs you will incur will be from your broker (you will have to ask them about fees).
Does this help?
Disclaimer
The material on this website is provided for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation or endorsement for any security or strategy, nor does it constitute an offer to provide investment advisory services by Quantopian. In addition, the material offers no opinion with respect to the suitability of any security or specific investment. No information contained herein should be regarded as a suggestion to engage in or refrain from any investment-related course of action as none of Quantopian nor any of its affiliates is undertaking to provide investment advice, act as an adviser to any plan or entity subject to the Employee Retirement Income Security Act of 1974, as amended, individual retirement account or individual retirement annuity, or give advice in a fiduciary capacity with respect to the materials presented herein. If you are an individual retirement or other investor, contact your financial advisor or other fiduciary unrelated to Quantopian about whether any given investment idea, strategy, product or service described herein may be appropriate for your circumstances. All investments involve risk, including loss of principal. Quantopian makes no guarantees as to the accuracy or completeness of the views expressed in the website. The views are subject to change, and may have become unreliable for various reasons, including changes in market conditions or economic circumstances.