Learn Italian: Questa è un'idea.

Because idea is a feminine noun that starts with a vowel. The feminine word for "a" or "an" is normally una. When a feminine noun begins with a vowel, una drops its last letter and replaces it with an apostrophe to make it easier to say: una idea becomes un'idea.

Is it wrong if I write un idea without the apostrophe?

Yes, in Italian spelling, the apostrophe here is required! The article un (no apostrophe) is only used for masculine words (like un amico). Because idea is feminine, you must use un' to show that it is a shortened version of una.

Why do we use Questa instead of Questo?

In Italian, words like "this" have to match the gender of the noun they describe. Because idea is a feminine noun, we use the feminine form Questa. If we were talking about a masculine noun, we would use Questo.

What is the difference between è with an accent and e without one?

The accent mark completely changes the meaning! With the accent (è), it means "is". Without the accent (e), it means "and".