[JJM Ballantyne]

"Is it correct to use the definite article before a name of a bridge?"

Unfortunately, the answer is: it depends.

We normally do not use an article when locations are used in the name of the bridge, so it's:

We walked across London Bridge

But we often use the article if the bridge has a particular description:

We walked across the Golden Gate Bridge

Confusingly, some allow both:

We walked across Sydney Harbour Bridge

We walked across the Sydney Harbour Bridge

"And is it also correct to say: 'Lake Balaton is the biggest in Europe'"

You can say this but it is rather ambiguous unless you've already indicated that you're discussing the subject of lakes:

There are a number of large lakes in Europe but Lake Balaton is the biggest.

Otherwise, it's perfectly acceptable to repeat yourself:

Lake Balaton is the biggest lake in Europe.

"'The Balaton is the biggest in Europe'?"

No, you wouldn't say this. No English speaker would say "The Balaton." They would say "Balaton" if it had already been established that this was a lake:

Yes, there are lots of lakes in Europe. But Balaton is the biggest.

Superior is the biggest of the Great Lakes.

Hope this helps!