What are the advantages and disadvantages of liberalism and radicalism?

The answer to this depends on what you mean by radicalism and especially liberalism (which can have totally different meanings depending on the context). I will focus on the definition of liberalism that is most commonly used today in this answer. 

Modern liberalism tends to focus on the constructive role of the state in protecting the environment, promoting economic opportunities for people, and preserving human rights. While most liberals accept that free enterprise and capitalism...

The answer to this depends on what you mean by radicalism and especially liberalism (which can have totally different meanings depending on the context). I will focus on the definition of liberalism that is most commonly used today in this answer. 

Modern liberalism tends to focus on the constructive role of the state in protecting the environment, promoting economic opportunities for people, and preserving human rights. While most liberals accept that free enterprise and capitalism are to be promoted, they believe that there are some things that are best managed by the state, often because they are unprofitable for private business. Liberals also tend to promote government involvement to promote equal opportunity for minorities in ways that conservatives find inappropriate. Criticisms of liberalism often argue, in general, that it reflects too much optimism about what government is able to accomplish. They say that government programs are too expensive and often yield unintended consequences that actually worsen the social problems they were supposed to address. Many critics also say that liberalism involves excessive government intervention in things best left to the private sector, and that it stifles the economy by restricting free enterprise. 

Radicalism can also have many different meanings. Whether far-left or far-right, radicals argue that society is so deeply flawed that it must undergo a fundamental, revolutionary change. Criticism of radical positions might include the following. Many would argue that radicalism assumes the ability of people to overthrow natural human institutions, to make things anew in a way that is impossible. Others decry the violence that often accompanies radical movements. Still others would say that in a democracy, radicalism draws votes away from more realistic mainstream political movements. Finally, radicals alienate moderates, making it difficult to form the types of coalitions that make political action possible. 

Again, it is important to note that the definitions of these words change with time and place. What is radical at one point in history, or in one society, is mainstream in another.